Question

Evaluate:

4 cos 80° cosec 10° + 5 sin 59° sec 31°

Answer 1

Given: 4 cos 80° cosec 10° + 5 sin 59° sec 31°.

Step-wise calculation:

1. `4  cos 80^circ  "cosec"  10^circ = 4 xx (cos 80^circ) xx (1/sin 10^circ)`

But cos 80° = sin 10°   ...(Since cos (90° – θ) = sin θ)

So, this term = `(4 xx sin 10^circ)/(sin 10^circ)` = 4.

2. `5  sin 59^circ  sec 31^circ = 5 xx (sin 59^circ) xx (1/cos 31^circ)`

But sin 59° = cos 31°   ...(Since sin θ = cos (90° – θ))

So, this term = `(5 xx cos 31^circ)/(cos 31^circ)` = 5.

3. Sum = 4 + 5 = 9.