Question

If sin θ = 3/5 and cos θ = 4/5 , find the value of sin2 θ + cos2 θ

Answer 1

Given:-

sin θ = 3/5

cos θ = 4/5

Solution:-

⏺️sin 2θ = 2.sin θ.cos θ

$sin 2θ = 2 \times \frac{3}{5} \times \frac{4}{5} = \frac{24}{25}$

⏺️cos2 θ = cos²θ - sin²θ

$cos2θ = {( \frac{4}{5} )}^{2} - {( \frac{3}{5} )}^{2} = \frac{7}{25}$

Therefore,

$cos2θ + sin2θ = \frac{24}{25} + \frac{7}{25} = \frac{31}{25}$