Question

The general solution of sin x − 3 sin2x + sin3x = cos x − 3 cos2x + cos3x is _________. Solution: sin x … If sec 4θ − sec 2θ = 2, then the general value of θ is __________. Solution: sec 4θ − sec 2θ = 2 ⇒ cos … If tan (cot x) = cot (tan x), then sin 2x = ___________. Solution: tan (cotx) = cot (tanx) ⇒ tan (cotx) = … If the solution for θ of cospθ + cosqθ = 0, p > 0, q > 0 are in A.P., then numerically the smallest …

Answer 1

Explanation:

We have, (sinx+sin3x)−3sin2x=(cosx+cos3x)−3cos2x

⇒2sin2xcosx−3sin2x=2cos2xcosx−3cos2x

⇒sin2x(2cosx−3)=cos2x(2cosx−3)

⇒sin2x=cos2x(Ascosx



=3/2)

⇒tan2x=1⇒tan2x=tanπ/4

⇒2x=nπ+

4

π

,n∈Z

x=

2

nπ

+

8

π

,n∈Z

Answer 2

Refer the Attachment

Hope it helps_