Question

If Cos2 64 +Cos2 A=1 then the angle A is____ ans is 26!!. I want the method!?​

Answer 1

Step-by-step explanation:

Given :-

Cos² 64° + Cos² A = 1

To find :-

Find the value of A ?

Solution :-

Method-1:-

Given equation is Cos² 64° + Cos² A = 1

=> Cos² A = 1 - Cos² 64°

=> Cos² A = Sin² 64°

Since Sin² A + Cos² A = 1

=> Sin² A = 1-Cos² A

=> Cos² A = Sin² (90°-26)°

=> Cos² A = Cos² 26°

Since Cos A = Sin (90°-A)

=>( Cos A)² = (Cos 26°)²

=> Cos A = Cos 26°

=> A = 26°

Method -2:-

Given equation is Cos² 64° + Cos² A = 1

=> Cos² 64° = 1- Cos² A

=> Cos² 64° = Sin² A

Since Sin² A + Cos² A = 1

=> Cos² 64° = Cos²(90°-A)

Since Sin A = Cos (90°-A)

=> Cos 64° = Cos (90°-A)

=> 64° = 90°-A

=> A = 90°-64°

=> A = 26°

Answer:-

The value of A for the given problem is 26°

Used formulae:-

→ Sin² A + Cos² A = 1

→ Cos A = Sin (90°-A)

→ Sin A = Cos (90°-A)

→ Sin² A = (Sin A)²

→ Cos² A = (Cos A)²