This question is from trigonometry topic trigonometric ratios on complementary angles in which we have been asked to calculate the value of θ, if cos2θ = sin4θ.
RS Aggarwal, Class 10, Chapter 12, question no 10
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cos2θ=sin4θ...(i)
we know that
sin(90°−θ)=cosθ
so equation (i) can be written as
sin(90°−2θ)=sin4θ
on comparing both sides
90°−2θ=4θ
⇒6θ=90°
⇒θ=15°
the value of θ=15o