Question

Solve this question for class 10th Trigonometry

Answer 1

Hi ,

Here I'm using x instead of theta .

cosx + sinx = √2 cosx ----( 1 )

Do the square of equation ( 1 ),

( cosx + sinx ) ² = ( √2 cosx )²

cos²x + sin² x + 2cosxsinx = 2cos² x

1 + 2cosxsinx = 2cos² x

2cosxsinx = 2cos²x - 1 -----( 1 )

Now ,

( cosx - sinx )²

= cos²x + sin²x - 2cosxsinx

= 1 - 2cosxsinx

= 1 - (2cos²x - 1 )

= 1 - 2cos² x + 1

= 2 - 2cos² x

= 2 ( 1 - cos² x )

= 2sin² x

Therefore ,

cosx - sinx = √ ( 2sin²x )

= √2 sinx

Hence proved .

I hope this helps you.

:)

Answer 2

Please mark brainliest...