If \cos A + \cos^2 A = 1, then find the value of \sin^2 A + \sin^4 A.... | VSA 2m | Maths | SuperPadhai

Introduction To Trigonometry > Question

VSA2 marksYear: 2023MediumCBSE Class 10

trigonometryidentitiestrigonometric-ratios

Question

If

cos A + cos^{2} A = 1

, then find the value of

sin^{2} A + sin^{4} A

.

Solution

1

cos A + cos^{2} A = 1 \Rightarrow cos A = 1 - cos^{2} A = sin^{2} A

+1 mark

2

∴ sin^{2} A + sin^{4} A = cos A + cos^{2} A = 1

(

∵ sin^{2} A = cos A

)

+1 mark

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