Question

Find the value of (sinθ+cosθ) ²+ (cosθ-sinθ) ²​

Answer 1

Step-by-step explanation:

it will be your answer of it

Answer 2

Given:

(sinθ+cosθ) ²+ (cosθ-sinθ) ²​

To find:

The value of (sinθ+cosθ) ²+ (cosθ-sinθ) ²​

Solution:

The value of (sinθ+cosθ) ²+ (cosθ-sinθ) ²​ is 2.

We can find the solution by following the given steps-

We know that the value can be obtained by using the property-

$(a+b)^{2} =a^{2} +b^{2} +2ab$

We know that the value of $sin^{2} theta+ cos^{2} theta=1$

The given expression=(sinθ+cosθ) ²+ (cosθ-sinθ) ²​

We will use the property to expand it.

On solving it, we get

=$sin^{2}$θ+$cos^{2}$θ+2sinθcosθ+ $cos^{2}$θ+$sin^{2}$θ -2sinθcosθ

=2($sin^{2}$θ+$cos^{2}$θ)

Putting the value,

=2(1)

=2

Therefore, the value of (sinθ+cosθ) ²+ (cosθ-sinθ) ²​ is 2.