Question

Prove that (sec theta + cos theta)^2+(sin theta - cos theta )^2=2

Answer 1

Step-by-step explanation:

Given: (sin∅+cos∅)²+(sin∅+-cos∅)²

To prove: =2

(sin∅+cos∅)²+(sin∅-cos∅)²

sin²∅+cos²∅+2sin∅ cos∅+sin²∅+cos2∅-2sin∅ cos∅

here,+2sin∅ cos∅ and -2sin∅ cos∅ gets cancelled

then,

sin²∅+cos²∅+sin²∅+cos²∅

The value of sin²∅+cos²∅=1

then,

1+1

⇒2.

Hence proved