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

Q: 1- cos 20+ sin 20 Prove tan e. 1+ cos 20+ sin 20

A: We can prove the given statement as below

Q: (cose – sin0)² = 1 – 2sin@cos0 %3D

A:

Q: Find 10. cos°0 do

A: Given:  Let I=∫0π cos6 θ dθ To Find: To evaluate the given integral.

Q: 1 - cos 20 58. Show that tan? 0 1 + cos 20

A: It is known that by double angle formula, 1-cos2θ=2sin2θ1+cos2θ=2cos2θ

Q: Express the number -5 in the form R(cos(0) + i sin(0)) = Reil where R>0 and 0 <0 < 2T.

A: rewrite -5 as -5=-5+0i comparing with z=a+bi a=-5 , b=0 R=a2+b2=-52+02=25+0=25=5 now…

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: Find the exact value of each expression. 1) cos-0 V3 3) cos- 5) sin- -1 7) cos-1 1 9) sin- 1 11) cos

A:

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

A:

Q: 7T 12 COS COS 뜸 + sin sin 5T 12

A:

Q: 3下 2 cos x 1-Sin x

A:

Q: 2. Prove the identity 2 cos²x 1-cos²x 2 tan² x

A: We will use the following identities,  and  We are asked to prove,

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

A: given  tanθ=-23,  cosθ&gt;0tanθ&lt;0  and  cosθ&gt;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: prove sin2 a/2=csc a-cot a/2 csc a

A:

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: 8. Prove that tan? 0 + cos? 0 + sin² 0 = sec² 0. %3D

A: Explanation and solutions is given below....

Q: 2 sin (45)+ 4 cos A 3

A:

Q: If cos a + cos B= a and sina + sin B= b, then show that 2 sin 2a + sin 2B = 2ab 1 a2 + b2

A: given: cosα+cosβ=asinα+sinβ=b we have to show that  sin2α+sin2β=2ab1-2a2+b2 R.H.S: 2ab1-2a2+b2…

Q: Show sin 3A = 3 sin A cos²A - sin A.

A: Explanation: Given that: sin3A=3sinAcos2A-sinA Concept: sin3A=3sinA-4sin3A sin2A+cos2A=1

Q: Since sin O O tan 1/12 = 1-cos 8 1+cos 0 1 Cos 0 2 " as tan 1-cos 0 tan/2 = √ 1+cos 0 COS /= ± √ ||…

A: Given :sinθ2=±1-cosθ2cosθ2=±1+cosθ2