cos(A+ B) cos² A – sin? B sec(A – B) =

Q: An equivalent exp a) cos² (0) COS O b) cot? (0)

A: We have to find the equivalent expression for   cos2(θ)( 1 + cot2(θ) ) from the following options :…

Q: Which of these is equal to cos 19? A) sin 71° B) sin 81° C. cos 71° D) Cos 81°

A: We have to find cos19

Q: Find the exact value of each expression.

A: Here we have to find the exact value of the given expression; sinπ12cos7π12-cosπ12sin7π12

Q: If cos 0 = 2/3, and tan < 0, what is the value of sin ? √21 2 O O - √21 2 √21 5 - 5 √21

A:

Q: Approximate to four decimal places, when appropriate.

A: Approximate to four decimal places, when appropriate. a) sin 45°b) sin 45c) cos3π/2°d)cos3π/2

Q: sin° (ec) cos" (eF) dc COS

A:

Q: Verify the identity. 5 cos? ß – 5 sin? ß = 10 cos? B – 5 5 cos? ß – 5 sin? ß = 5 cos? ß – 5 (1 - = 5…

A:

Q: If cos(a) = 2/3 , sin(b) = -3/5, P(a) in Q1, P(b) in Q3,  find sin b/2

A:

Q: 3. If 0° < 0< 90° and sin e = , find cos 20. 50 81 56 81 81

A:

Q: Prove that the equation is an identity. 6 sin? t – 6 cos2t = 6 - 6 cot² t 1 + cot? t

A:

Q: sin? x – cos? x 1. tan x – cot x = sin x cos x

A:

Q: "III. Find the value of the expression. 12.) csc 300• cos 60 sec 150° · sin 120°

A: SOLUTION-

Q: Rewrite sin(a−7π/4)in terms of sin(a) and cos(a).

A: Given the query is to rewrite the ue expression.

Q: If Sin A = where "< A < 1,Sin B = 5 where 0 < B<: 2 13 then find Tan (A+B), Cos(A-B)

A: Given that sinA = 4/5 where (π/2) &lt; A&lt; π  and  SinB= 5/13 where 0&lt; B&lt;( π /2) We have to…

Q: Verify the identity. (Simplify at each step.) (1 + sin a)(1 – sin a) = cos? (1 + sin a)(1 - sin a) =…

A: Simplification

Q: Use words to describe the given formula, cos * cos * = (1/2) [cos(*- *) + cos(* + *)]

A: We know that cos(A+B)=cosAcosB - sinAsinB           ...(1) cos(A-B)= cosAcosB + sinAsinB…

Q: If cos(a) = 2/3 , sin(b) = -3/5, P(a) in Q1, P(b) in Q3,  find cos2(b)

A:

Q: 4(cos 240°+ i sin 240°)

A: Given complex number is   4cos240o+isin240o

Q: 1 – sin? B 47. cos B cos B

A:

Q: T/6 The value of cos* 30 sin 60 de is COS

A:

Q: If cos² 9x sin 91 = cos B, then B =

A: Given Problem:- ifcos29x-sin29x=cosBthen find B

Q: Verify the identity. (Simplify at each step.) (1 + cos a)(1 – cos a) = sin? a (1 + cos a)(1 – cos a)…

A: Given:  1+cos α1-cos α=sin2 α To Find: To verify the given identity.

Q: Verify the identity. (Simplify at each step.) (1 + cos a)(1 – cos a) = sin² a %3D (1 + cos a)(1 -…

A:

Q: sin?A = 01- cos?A cos?A - 1 1+ cos?A

A:

Q: Verify the identity. (Simplify at each step.) (1 + cos a)(1 – cos a) = sin² a (1 + cos a)(1 – cos a)…

A:

Q: 8. Verify the identity: 1- cos h sin? h h h(1 + cos h)

A: To verify:1-coshh = sin2hh1+coshUseful for the question:  sin2x + cos2x = 1a2 - b2 = a-ba+b

Q: If 0° <0<90° and cos @ = , find cos I3I

A:

Q: 12. Verify the identity by transforming the right side of the equation into the left side. Show all…

A: Our Aim is to verify the identity given below:-cot2 (x)=cosec2 (x)-cosec2 (x) sin2 (x) -(i)

Q: 6- If sinA=-3/5, 0<A<2n and cosB = -1/5 0< B<2n, find the exact value of cos(A+B) !

A: Solution:-

Q: Evaluate the integral.

A:

Q: Write the formulas for cos(A - B) and sin (A - B)?

A: We have to write the formulas for cosA-B and sinA-B. We know the formula for cosine difference angle…

Q: Verify the identity. 4 cos?(x) – 2 = 2 – 4 sin2(x)

A:

Q: Evaluate cos |a+ 3 if sin a = 3 and a is in quadrant II.

A:

Q: 5. cos 20 = cos²0 – ! 2

A:

Q: Find the exact value of : a) cos 60° = b) tan c) sin 45° = 4 e) sec0° = d) cos T =

A: Lets find exact value of given trigonometric function.

Q: -) Prove the identity. 1+ sin ß cos ß cos B + 1+ sinß 2 sec B %D

A:

Q: The term cos(2a) can also be written as ... O 2 cos? a – 1 2 sin a – 1 O2 sin a cos a sin? a + cos?a

A: Let, cos2α=cosα+α Since, cosA+B=cosAcosB-sinAsinB

Q: 11.) / sin? 0 + cos? 0 do cos 0

A: The objective is to evaluate the integration.

Q: Find the exact value of the expression. 11T cos 12

A: To find : The exact value of the expression cos11π12. Formula used: cosx+y=cosxcosy-sinxsiny…

Q: 11) cos? 0 = 2+ 2sin 0

A: Given query is to find the value of angle theta.

Q: Rewrite (csc? e-1)(1- cos e) in terms of cos 0, and simplify. A 1-2cos?e C cos e 1-2cos? e+ cos*e D…

A:

Q: 10. Use the formula cos(2a) = 1 – 2 sin? æ to find cos , if sin O v2 2 O v? 2 O_1 2

A: Given that       cos(2x) = 1 - 2sin2(x)  and sin(pi/4)=√2/2 Here we have to find cos(pi/2).

Q: Given cos² x = a, where –1< a < 1. what is the value of cos 2x? O 1 01– 2a О 2а - 1 O 2a

A: We can find the answer as below

Q: If sin A = 3/5 with A in QI and cos B = - 5/13 with B in QIII, find sin (A + B), cos (A + B), and…

A: sinA=35  &amp;  cosB=-513 Now by using the identity sin2A+cos2A=1, we get…

Q: If (cos* a/cos? B) + (sin“ a/ sin B) = 1, then prove that (cos* B/ cos? a) + (sin? B/ sin? a) = 1 2

A: Given: cos4αcos2β+sin4αsin2β=1 To prove that  cos4βcos2α+sin2βsin2α=1

Q: . If A<2 sin-1x+ cos¬1x < B then A = -2 B b. A= 0, В — п c. A = -. Зл B = 2 Зл d. A= 0, B = e. None…

A: Given  We know that Also, we know that range of is [-pi/2,pi/2] Therefore,

Q: Which of the following is TRUE? A. 1- sin ? = cos? cos 2 B. 1- cos? 20 = sin² 20 C. 1 – tan? = sec?…

A:

Q: COS Coso xdxx

A: ∫cos6x dxApplying reduction formula with n=6 := cos5x sinx6 + 56∫cos4x dxApplying reduction formula…