Q41 of 268 Page 5

If secθ + tanθ=m and sec θ – tanθ = n, then prove that

Given : sec+tan=m and sec –tan=n

To Prove : √mn = 1

Taking LHS = √mn

Putting the value of m and n, we get

Using the identity, (a + b) (a – b) = (a² – b²)

=√(1) [∵ 1+ tan² θ = sec² θ]

=±1

=RHS

Hence Proved

Prove the following identities

If cosθ + sinθ = 1, then prove that cosθ – sin θ = ± 1.

If sinθ + sin²θ = 1, then prove that cos²θ +1 cos⁴θ = 1