Question

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I want answer of question no.14 nd 15 plzzzz...☺✌

Answer 1

Hey !!!

Q. 14

sinx + sin²x = 1 ( given)

sinx = 1 - sin²x

sinx = cos²x -----1)

Squaring on both side then

sin²x = cos⁴x -----2)

hence ,

sinx = sin²x = cos²x + cos⁴x = 1

hence, we can say that

cos²x + cos⁴x = 1 prooved ♻

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15 no. Question

solution :-

cosx + sinx = √2cosx -----1)

cosx + sinx and cosx - sinx Squaring and adding both

we get

(cosx + sinx )² + ( cosx - sinx ) ²

cos²x + sin²x + 2sinx × cosx + cos²x + sin²x - 2sinxcox

= 2 ------2)

now adding and Squaring again both equation

(cosx + sinx ) ² + ( cosx - sinx ) ²

(√2cosx )² + ( cosx - sinx ) ² = 2

[here cosx - sinx = √2cosx is given ]

2cos²x +( cosx - sinx )²= 2

(cosx - sinx )² = 2 - 2cos²x

(cosx - sinx)²= 2 ( 1 - cos²x )

(cosx - sinx )² = √2sinx Rhs prooved


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Hope it will help you !!!

@Rajukumar111