Question

please solve this question as soon as possible.....its very important for 10th cbse board

Answer 1

To prove:cos∅+sin∅=√2 sin∅
Proof: LHS=
cos∅-sin∅=√2sin∅
cos∅=√2sin∅+sin∅
cos∅ = sin∅(√2+1)
sin∅=cos∅/(√2+1)
on rationalising we get sin∅=cos∅×(√2-1)÷(√2+1)×(√2-1)
sin∅=cos∅×(√2-1)÷(√2)²-(1)²
sin∅=√2cos∅-cos∅
sin∅+cos∅=√2cos∅
=RHS Hence proved

I hope that it is very important question for class 10 for board examination and you definitely know many solutions to take advise to me.
And also rate it as brainlest question.