V5 sec² 0 V5 sec 0 Why is = sec 0? Because sec2 0 = (sec 0) (sec 0) Because sec2 0 = tan² 0 1 Because sec 0 = Cos 0

Q: tan 0+sec 0-1 1+sin e 8. %3D tan 0-sec 0+1 cos 8 Proof:

A: Topic:- trigonometry

Q: sec2 0 – (sec 0 + tan 0)(sec 0 – tan 0) cos? 0 cos² 0 = 1

A:

Q: Establish each identity.

A: The given identity is,  1-cos θsin θ+sin θ1-cos θ=2 csc θ The objective is to establish the…

Q: i) tan 0 + tan 0 = 0 iii) 3 Cos 0 + 2 Sec 0 +7= 0 (ans.:i)-180,-45,0,135,180; ii)-90,11.5,90,168.5;…

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Q: tan2(0) csc²(0) – 1 5) sec2 (0) sin (0)

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Q: Establish each identity.

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Q: 1- sec 0 9. I. cos 0 -1 tan 0 sin 0 cos 0 + sin 0 II. sec 0 + csc 0 = cos 0 sin 0

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Q: Sinh exp 2 ()- i sin 1 i sinh 1 -i sinh 1 -i sin 1

A:

Q: cos 2x-1 i) x sin 2x 2 tan 30–20 ii) tan 40

A: follow next step.

Q: Sin 0= 4. tan 0>0 Part 1 of 3 (a) sin 20 = Part 2 of 3 (b) cos 20=

A:

Q: Quadrants of: cos-0>0, sin -0>0   Quadrants of: cos 0>0, csc 0<0

A: We have to find quadrant

Q: cos 0+cos 0 tan 0

A: 1+ tan²θ = sec² θ    cos θ = 1/ sec θ   use both we will simplify

Q: sec²0 – sin²Øsec²0 = 1

A: Given expression: sec2θ-sin2θsec2θ=1 Taking the L.H.S of the equation ⇒sec2θ-sin2θsec2θ

Q: Q.3) Prove that L-1 ) =(coshat sinat + sinhat cosat) %3D 2a +4a

A:

Q: 1.secB-cosB = tanB sin B 2.cotAcosA + sin A= cscA

A:

Q: Establish each identity given in attachment.

A: An identity is true if one side of the identity can be converted to another and vice versa. So to…

Q: ((/sin3z – cos2zV sin3z + cos2z bz

A: The objective is to solve the integration ∫sin3z-cos2zsin3z+cos2zdz Now,…

Q: 6. tan*e + tan²0 = sec*0 – sec²0 sec20 7. 1- sin A 1+ sin A (sec A – tan A)² tan0 + sece-1 8. tane -…

A: To prove the given identities we have to use some basic trigonometric formulas

Q: (sec^ 2 beta-1).tan( pi/2 - beta)=tan beta

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Q: 1- cos 0 + sin 0 sin 0 2 csc 0. 1- cos 0 |

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Q: sin 20 + 2 cos 2 0 Verify the identity tan 0 + 2 cot 0 = sin 0 cos 0

A: Solve the given identity

Q: (sec 0 + csc 0)(cos 0 – sin 0)

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Q: sec 0 – cos 0 = sin 0 tan 0

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Q: V3 Tan" (-V3) Cos"(-1) 3. Sin 2 1. 2.

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Q: csc 0 – cot 0 3. secu+tanu 5. secu – tanu (sinu+1)² = cot e 4. cot 0 + tan 0 = csc 0 sec 0 sec 0 – 1…

A: Topic-Trigonometry

Q: Differentiate

A: Given: the function

Q: cos 즙 V2+v3 V2 and sin = V2- 23. cos를

A: #23 Recall:  cos2x+sin2x=1  ⇒cos x=1-sin2x Given,  sin π8=2-22 To find, cos π8

Q: 6. cos A = - 17 and cos B = -, with A and B in QIII.

A:

Q: sec(0) = cot(0) = (b) y (1, -1) sin(0) = cos(0) = tan(0) = csc(0) = sec(0) = cot(0) =

A:

Q: Establish each identity.

A: To prove:sec4θ - sec2θ = tan4θ + tan2θ

Q: Verify the identity.

A: (sec2θ-1)cotθtanθsinθ+cosθ=sinθ

Q: cos (0) tan (0)+3tan(0)=0

A: cosθtanθ+3tanθ=0

Q: ) cos(cos-¹(35)) ) sec(tan-¹(5)) csc(sin-¹(n)) ) cos ¹(cos(29°)) (4π) 5 =) sin ¹[sin ]]

A:

Q: Q.3) Prove that L-1 ( = (coshat sinat + sinhat cosat) 4+4a+.

A:

Q: sin (-8-2T) Sec co) arc tan (x) TT cos' (Gw) Sin' GW) dw CoS tant (2) sec (2)dz

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Q: cos/ 3 17 cos (TA +x) tanx

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Q: sin 4t – sin 2t = tan t cos 4t – cos 2t

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Q: sin 0 = tan 0>0 Find the exact value of sec 0. 4.

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Q: Verify the identity.

A: Given: verify the identity cos3x+cos5xcos3x-cos5x=cotxcot4x we know that…

Q: المو Sin 2 0 CosG %3D Sin o COSG

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Q: Cos 0–N1+ Sin 20 Tan 0 Sin 0 –/1 + Sin 20 N.

A: Recall: sin (2θ)= 2 sinθ cosθ sinθ cosθ= tanθ cos2θ+sin2θ=1

Q: Simplify tan(arctan 1/3 ). 1/3 -1/3 no solution

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Q: sin cos 4 12 cos sin 12 4

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Q: tan 0+sec 0-1 %3D 1+sin 0 8. tan 0-sec 0+1 cos 0 Proof:

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Q: Find the quadrant containing u if the given conditions are true.

A: (a) we know that, the tan θ&gt;0 if θ is in Quadrant II or iv, and also cos θ&gt; 0 if θ is in…

Q: Cos 0/2 -cos 0=1

A:

Q: cos –1 (-V)] 2 sec OS

A: Simplification