Question

If θ is a positive acute such that sec θ = cosec 60°, find the value of $2cos^{2}\Theta-1$.

Answer 1

SOLUTION :  

Given : sec θ = cosec 60° and  θ is positive acute angle .

sec θ = cosec 60°

cosec (90 - θ) = cosec 60°

[cosec (90 - θ) = sec θ]

On equating both sides,

(90 - θ) = 60°

θ = 90° - 60°

θ = 30°

We have to find a value :  2cos²θ - 1  

2cos²θ - 1  

Put θ = 30°

2cos²θ - 1  = 2 × cos² 30° - 1

= 2 × (√3/2)² - 1  

[cos 30° = √3/2]

= 2 × ¾ - 1

= 3/2 - 1

=( 3 - 2)/2

= ½

Hence, the value of 2cos²θ - 1 is ½ .

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Answer:

Step-by-step explanation: