Question

sin 2 a + cos 2 a is​

Answer 1

Answer:

1

Step-by-step explanation:

To Find :-

Value of :-

sin²A + cos²A

How To Do :-

Here they are asked us to find the value of 'sin²A + cos²A'. As we know that formula of 'sinA' and 'cosA' . We need to find the value of 'sin²A and cos²A' by squaring those values . After that we need to add those values and by applying Pythagoras theorem formula we can obtain that value.

Formula Required :-

sinA = opposite side/hypotenuse side

cosA = adjacent side/hypotenuse side

Pythagoras theorem :-

(hypotenuse side)² = (opposite side)² + (adjacent side)²

Solution :-

sinA = opposite side/hypotenuse side

Squaring on both sides to the above equation :-

(sinA)² = (opposite side/hypotenuse side)²

sin²A = (opposite side)²/(hypotenuse side)²

cosA = adjacent side/hypotenuse side

Squaring on both sides to the above equation :-

(cosA)² = (adjacent side/hypotenuse side)²

cos²A = (adjacent side)²/(hypotenuse side)²

sin²A + cos²A :-

Substituting the values :-

= (opposite side)²/(hypotenuse side)² + (adjacent side)²/(hypotenuse side)²

$=\dfrac{(opposite\:side)^2+(adjacent\:side)^2}{(hypotenuse\:side)^2}$

= (hypotenuse side)²/(hypotenuse side)²

[ ∴ (hypotenuse side)² = (opposite side)² + (adjacent side)² ]

= 1

∴ sin²A + cos²A = 1