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

Q: establish each identity.

A: To prove the identity: sinθ-cosθ+1sinθ+cosθ-1=sinθ+1cosθ Proof: We know that, sin2θ+cos2θ=1 Left…

Q: sin(2r) dr 9- cos (2.x)

A: Integrate

Q: sin 0 cos Od0 -u'du FC = - 1 cos“ 0 + C 19.

A:

Q: Establish each identity.

A:

Q: (1+sin2x)/(sin2x)=1+(1/2)(sec x)(csc x) prove identity

A: Left hand side:1+sin(2x)sin(2x)=1sin(2x)+sin(2x)sin(2x)=1sin(2x)+1=12sin(x)cos(x)+1  [using double…

Q: cos x-cos(5x) Prove identity: tan(2x) sin x+sin(5x)

A:

Q: sin(2n – 1)x dx , Un %3D sin x

A: Yghhhhhhg

Q: Sin 0/1 + co² B) 2.

A: sinθ1+cot2θ                             =sinθ1+cos2θsin2θ…

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: cos( – x) + tan( – x)sin( – 2)

A:

Q: COS X 3) sec x + tan x = 1 - sin x

A:

Q: Establish each identity.

A: To establish the identity: sinθ+cosθ2+sinθ-cosθ2=2 Proof: We have identity, a+b2=a2+b2+2ab…

Q: sec e de 1+ tan 0

A: To find∫secθ1+tanθdθ

Q: | sin' cos“ 4 x

A:

Q: sin (z+ in terms of sin(x) and cos(r). 4 Rewrite sin + -

A: Topic = Trigonometry

Q: sin x(cos x-1) 8. Prove sin(n -x) – tan(t + x) | COSX

A:

Q: sin*[In()ax x{cos[

A: Given : ∫ sin3ln72x4dxxcosln72x4-1 Let us take  u= ln72x4⇒dudx= -4x⇒dx=-x4du Therefore, ∫…

Q: 4. sin(4x) = (4 sin(x) cos(x))(2(cos(x))² – 1) %3D

A:

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: sin x a) 1+cos2 x dx

A:

Q: snip

A:

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

A: Note the formula:

Q: Evaluate the integral.

A:

Q: (sin 0 + cos 0)´ =1+ sin(20) s 0)° =1+sin(20)

A:

Q: . sin 2x cos x+ cos 2 sin x = 12

A:

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

A:

Q: I+ cosx+ cos 2x (ii)Show that sin x+ sin 2x tan 20 - tan 0 = tan 0 sec20 cotx (iii) (iv) (cose -…

A:

Q: sin x.cos x 1+ 2.In x

A:

Q: cos(x+π6)+sin(x−π3)=______

A:

Q: المو Sin 2 0 CosG %3D Sin o COSG

A:

Q: sin 0(1 + tan 0) tan 0(sin0 +cos0)

A:

Q: sin'x cos'xdk 3. X COS

A: It is given that, ∫sin2xcos3x dx We have to solve it.

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: sin x+ tan x sin (2x) 5. Determine the non-permissible values of the identity 1+ cos x 2 cos x Cos3x…

A: Solve using properties trigonometric identities

Q: sin 0 13. Prove that 1 - = Csc 0(1 + cos 0). Cos 0

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Q: sin e, sine cose cose 1 tan 2 0 O2 cot 0 2 tan 0

A:

Q: #/2 sin " x 2: Evaluate 20 sin ° x+ coSx

A:

Q: I+ Sin X COSX 32see* COS X + Sin X

A: This problem can be solved by simplification through trigonometric identities.

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

A:

Q: sin 0 sin 0 2 1- cos 0 1+ cos e tan 0

A:

Q: stion Three: If y = sin(x) – sin³ (x). show that y' = cos³(x).

A: We will differentiate the function and use the identity : 1 - sin²(x) = cos²(x)

Q: cos x + 2 sin x cos x = 0

A:

Q: 1+sin A cos 2 sec u – cos µ = sin µ tan µ 4. + 2 sec 1 %3D cos A 1+sin A

A: We have to verify the given identities.

Q: (a) cos (tan (1)) = V2 (b) sin cos 2.

A: