Question

if cos square theta minus sin square theta is equal to tan square alpha then prove that cos square alpha minus sin square alpha is equal to tan square theta

Answer 1

Answer:

Proved if Cos²θ - Sin²θ = tan²α then Cos²α - Sin²α = tan²θ

Step-by-step explanation:

if Cos²θ - Sin²θ = tan²α

Then

Cos²α - Sin²α = tan²θ

LHS = Cos²α - Sin²α

= Cos²α(1 - Tan²α)

= (1/Sec²α) (1 - Tan²α)

Sec²α = 1 + Tan²α

= (1/(1 + Tan²α))(1 - Tan²α)

= (1 - Tan²α)/(1 + Tan²α)

putting value of Tan²α

= (1 - (Cos²θ - Sin²θ))/(1 + Cos²θ - Sin²θ)

= (1 - Cos²θ + Sin²θ))/(1  - Sin²θ + Cos²θ)

using 1 - Cos²θ = Sin²θ & 1  - Sin²θ = Cos²θ

= (Sin²θ + Sin²θ))/(Cos²θ + Cos²θ)

= 2Sin²θ/2Cos²θ

= tan²θ

= RHS

Proved

Answer 2

Answer:

May be this will help you ... It's is of basic trignomentry .......