Question

if 0 is a positive acute angles such that are 0=cosec 60,find the value of 2 cos2 0-1

Answer 1

Question

If θ is a positive acute angles such that are sec θ = cosec 60°, find the value of 2 cos²θ - 1.

Solution

Method - 1 :-

sec θ = cosec 60°

⇒sec θ = 2/√3

As cosec 60° = 2/√3.

⇒sec 30° = 2/√3

Hence, θ = 30°.

Method - 2 :-

sec θ = cosec 60°  

⇒cosec (90 - θ) = cosec 60°  

As cosec (90 - θ) = sec θ]

, and vice-versa.

⇒(90 - θ) = 60°  

Same bases get cancelled.

⇒θ = 90° - 60°  

⇒θ = 30°

$\rule{180}2$

Putting the value of θ = 30° in 2cos²θ - 1 :-

2cos²θ - 1

= 2 × (cos30°)² - 1

= 2 × (√3/2)² - 1

= (2 × 3/4) - 1

= 3/2 - 1

= (3 - 2)/2

= 1/2         ...ANSWER