Question

cos15°cos45°2cosec75°​

Answer 1

Step-by-step explanation:

Given:-

cos15°cos45°2cosec75°

To find:-

Find the value of cos15°cos45°2cosec75°

Solution:-

Given that :

Cos15° Cos45° 2 Cosec75°

It can be written as

Cos15° Cos45° 2 Cosec(90°-15°)

We know that

Cosec (90° - A) = Sec A

=> Cos15° Cos45° 2 Sec 15°

We know that

Sec A = 1 / Cos A

=> Cos15° Cos45° 2 (1 / Cos 15°)

=>( Cos 15°/ Cos 15°) Cos 45° ×2

=> (1) Cos 45° ×2

=> Cos 45° × 2

=> (1/√2) × 2

=> 2/√2

On multiplying the numerator and the denominator with √2

=> (2/√2)×(√2/√2)

=> (2×√2)/(√2×√2)

=> (2√2)(√2)^2

=>2√2/2

=> √2

Answer:-

The value of Cos15° Cos45° 2 Cosec75° is √2

Used formulae:-

• Cosec (90° - A) = Sec A

• Sec A = 1 / Cos A

• Cos 45° = 1/√2