Question

sin^2(25°) + sin^2(65) =_____​

Answer 1

Step-by-step explanation:

Given:-

Given expression is sin^2(25°)+sin^2(65°)

To find:-

Find the value of sin^2(25°) + sin^2(65°)?

Solution:-

Metgod-1:-

Given expression is sin^2(25°) + sin^2(65°)

It can be written as

(Sin 25°)^2 + (Sin 65°)^2

=> [Sin (90°-65°)]^2 + (Sin 65°)^2

We know that

Sin (90°-A) = Cos A

=> (Cos 65°)^2+(Sin 65°)^2

=> (Sin 65°)^2 + (Cos 65°)^2

=> Sin^2 65° + Cos^2 65°

We know that

Sin^2 A + Cos^2 A = 1

=> Sin^2 65° + Cos^2 65° = 1

Method-2:-

Given expression is sin^2(25°) + sin^2(65°)

It can be written as

(Sin 25°)^2 + (Sin 65°)^2

=> (Sin 25°)^2+[Sin (90°-25°)]^2

We know that

Sin (90°-A) = Cos A

=> (Sin 25°)^2+(Cos 25°)^2

=> Sin^2 25° + Cos^2 25°

We know that

Sin^2 A + Cos^2 A = 1

=> Sin^2 25° + Cos^2 25° = 1

Answer:-

The value of sin^2(25°) + sin^2(65°) is 1

Used formulae:-

• Sin (90°-A) = Cos A

• Sin^2 A + Cos^2 A = 1