Evaluate the following: sin 36 ° cos 54 ° + sec 31 ° cosec 59 ° - Mathematics

Evaluate the following: `(sin36°)/(cos54°) + (sec31°)/("cosec"59°)`

Sum

`(sin36°)/(cos54°) + (sec31°)/("cosec"59°)`

= `(sin(90° - 54°))/(cos54°) + (sec(90° - 59°))/("cosec"59°)`

= `(cos54°)/(cos54°) + ("cosec"59°)/("cosec"59°)`

= 1 + 1
= 2.

shaalaa.com

Trigonometric Equation Problem and Solution

Is there an error in this question or solution?

Chapter 27: Trigonometrical Ratios of Standard Angles - Exercise 27.3

Chapter 27 Trigonometrical Ratios of Standard Angles
Exercise 27.3 | Q 3.1

Calculate the value of A, if (sec 2A - 1) (cosec 3A - 1) = 0

If sin 3A = 1 and 0 < A < 90^°, find cos 2A

If A = B = 60°, verify that: cos(A - B) = cosA cosB + sinA sinB

If A = B = 60°, verify that: tan(A - B) = `(tan"A" - tan"B")/(1 + tan"A" tan"B"")`

If `sqrt(3)` sec 2θ = 2 and θ< 90°, find the value of

cos² (30° + θ) + sin² (45° - θ)

Evaluate the following: `(sin62°)/(cos28°)`

Evaluate the following: sin22° cos44° - sin46° cos68°

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

Express each of the following in terms of trigonometric ratios of angles between 0° and 45°: cos84° + cosec69° - cot68°

If tan4θ = cot(θ + 20°), find the value of θ if 4θ is an acute angle.