Question

If sin x = `7/25`, where x is an acute angle, then find the value of sin x ⋅ cos x (tan x + cot x).

Answer 1

sin x ⋅ cos x (tan x + cot x)

= `sin x ⋅ cos x(sin x/cos x + cos x/sin x)`

= `sin x ⋅ cos x ((sin^2x + cos^2x)/(cos x ⋅ sin x))`

= `sin x ⋅ cos x(1/(cos x ⋅ sin x))`

= 1 (Constant)

Since the value of sin x ⋅ cos x (tan x + cot x) is constant, it is equal to 1 for all angles.