Prove that Cos θ/Sin(90° - θ) + Sin θ/Cos (90° - θ) = 2

Prove that `cos θ/sin(90° - θ) + sin θ/cos (90° - θ) = 2`.

Sum

LHS = `cos θ/sin(90° - θ) + sin θ/cos (90° - θ) `

= `cos θ/cos θ + sin θ/sin θ`

= 1 + 1 = 2

= RHS

Hence proved.

shaalaa.com

Is there an error in this question or solution?

Prove the following identities:

sec⁴ A (1 – sin⁴ A) – 2 tan² A = 1

Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`

If sin θ − cos θ = 0 then the value of sin⁴θ + cos⁴θ

Without using trigonometric table , evaluate :

`cosec49°cos41° + (tan31°)/(cot59°)`

Without using trigonometric table , evaluate :

`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`

If a cos θ – b sin θ = c, then prove that (a sin θ + b cos θ) = `± sqrt(a^2 + b^2 - c^2)`

cos θ . sec θ = ?

`sin θ = 1/2`, then θ = ?

Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.

`1/sin^2θ - 1/cos^2θ - 1/tan^2θ - 1/cot^2θ - 1/sec^2θ - 1/("cosec"^2θ) = -3`, then find the value of θ.