What is the value of 6tan^2θ - 6/cos^2θ ?

Question

What is the value of 6tan²θ - \(\frac{6}{cos^2θ}\) ?

Answer 1

To find: 6tan²θ - \(\frac{6}{cos^2θ}\) 

∵ secθ = \(\frac{1}{cosθ}\) 

⇒ sec²θ = \(\frac{1}{cos^2θ}\)

⇒6tan²θ - \(\frac{6}{cos^2θ}\) = 6tan²θ -6sec²θ = 6(tan²θ - sec²θ)

Now, as 1 + tan²θ = sec²θ 

⇒ tan²θ – sec²θ = – 1

⇒ 6tan²θ - \(\frac{6}{cos^2θ}\) = 6(tan²θ - sec²θ) = 6(-1) = - 6