Question

if sin theta + cos theta is equal to X and secant theta + cos secant theta is equal to Y then prove that x square - 1 is equal to 2 X upon y

Answer 1

Let theta represent by €.

sin€ + cos€ = x

1 + 2sin€cos€ = x2

sin€cos€ = x2- 1/2. equation (1)

Given: cosec€ + sec€ = y

1/sin€ + 1/cos€ = y

sin€ + cos€/y = sin€cos€

x/y = x2-1/2. by equation (1)

2x/y = x2-1

Hence proved.