Evaluate the following: tan 42 ° cot 48 ° + cos 33 ° sin 57 °

Evaluate the following: `(tan42°)/(cot48°) + (cos33°)/(sin57°)`

Sum

`(tan42°)/(cot48°) + (cos33°)/(sin57°)`

= `(tan(90° - 48°))/(cot48°) - (cos(90° - 57°))/(sin57°)`

= `(cot48°)/(cot48°) - (sin57°)/(sin57°)`

= 1 - 1
= 0.

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Trigonometric Equation Problem and Solution

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Chapter 27: Trigonometrical Ratios of Standard Angles - Exercise 27.3

Chapter 27 Trigonometrical Ratios of Standard Angles
Exercise 27.3 | Q 3.2

State for any acute angle θ whether sin θ increases or decreases as θ increases

From the given figure,
find:
(i) cos x°(ii) x°(iii) `(1)/(tan^2 xx°) – (1)/(sin^2xx°)`
(iv) Use tan x^o, to find the value of y.

Solve the following equation for A, if 2 sin 3 A = 1

Solve the following equation for A, if `sqrt3` cot 2 A = 1

If θ = 30°, verify that: 1 - sin 2θ = (sinθ - cosθ)²

Evaluate the following: `((1 - cosθ)(1 + cosθ))/((1 - sinθ)(1 + sinθ)` if θ = 30°

Evaluate the following: `(tan12°)/(cot78°)`

Evaluate the following: tan(78° + θ) + cosec(42° + θ) - cot(12° - θ) - sec(48° - θ)

Evaluate the following: `(sin0° sin35° sin55° sin75°)/(cos22° cos64° cos58° cos90°)`

Prove the following: sin²30° + cos²30° = `(1)/(2)sec60°`