sin 0(3sin? 0+ 4cos? 0) = 3 cos 0 + cos³ 0 4. Prove that tan 0

Q: sin 2x Verify 1+ cos 2x = tan x.

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Q: sin? x 1- 1-cos x =-COS X

A: Here we have to use the basic trigonometric identity sin2θ+cos2θ =1 and we know that  a2-b2=…

Q: (cose – sin0)² = 1 – 2sin@cos0 %3D

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Q: Find all solutions to 10 cos2 r-13 cos T = -4 sec2 r+4 tan? r on 0, 27.

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Q: What is the exact value of 2sin(x/2) * cos(x/2) if sin of x = 3/5 and cos of x = 4/5 ?

A: To determine the exact value of the expression.

Q: Show that sin ( 40) (cos 0) (4 sin 0 – 8 sin³ 0). %3D

A: To show: That sin 4θ=cos θ4 sin θ-8sin3θ. Formula used: sin A+B=sin A·cos B+sin B·cos A cos…

Q: 3. Matching a. r = 4 – sin 40 b. s = 1 – 4 sin 40 %3D C. r = 1+4cos 40 d. r = 4+ cos 40

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: 12 Prove that sin 80 cos 0-sin 60 cos 30 a. = tan 20 cos 20 cos 0- sin 30 sin 40

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Q: Proving Identities. Verify the identity. (1-sin²t+ cos² t)² +4sin² t cos² t = 4cos² t

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Q: sin e cos (cos a cosec 0) de (1-cos a). 2 ||

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Q: (cos x +i sin a)" = cos nx +i sin na -1)

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Q: 7T 12 COS COS 뜸 + sin sin 5T 12

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Q: 2 cos 0 d 1 - sin A

A: We can find the integration as below.

Q: Find sin 8. tan 0 = √2 w|n 3 cos 8>0

A: given  tanθ=-23,  cosθ>0tanθ<0  and  cosθ>0, there for θ is in 4th quadrant

Q: 2 2 cos 0 d0 V1 – sin 0

A: Given:        ∫0π2cosθ1-sinθdθ substitute u=1-sinθ→dudθ=-cosθ→dθ=-1cosθdθ      =∫10-1udu…

Q: Q4: Prove that: cos?x – sin?x cos²x - 1- tan?x

A: We need to prove that cos2x-sin2xcos2x=1-tan2x We will use tanx =sin xcos x

Q: Show that sin² 0 cos² 0 8 1 cos (40). 8

A: To show that: sin2θcos2θ=18-18cos(4θ) Solution: We know: 2sinxcosx=sin(2x)    ..(1)cos(2x)=1-2sin2x…

Q: Show that V2 + V2 cos 2 and cos 16 and use it to find sin 16 Show that

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Q: 4л coS 씀Cos 즙Cs -sin sin 15 15 15

A: We have to find the exact value cosπ15cos4π15-sinπ15sin4π15.

Q: cos A+1 cSc A %3D sin' A 3 1-cos A

A: Consider the given identity, cosA+1sin3A=cscA1-cosA Cross multiply the equation,…

Q: tan(C + A)tan(C – A)tan(B+ D) = tan(D – B)

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

A: