Find the value of 'x' in each of the following:

Sum

From the figure, we have

sin x = `"BC"/"AC"`

⇒ sin x = `(15/sqrt(2))/(15)`

⇒ sin x = `(1)/sqrt(2)`
⇒ sin x = sin45°
⇒ x = 45°.

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Trigonometric Equation Problem and Solution

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Chapter 27: Trigonometrical Ratios of Standard Angles - Exercise 27.2

Chapter 27 Trigonometrical Ratios of Standard Angles
Exercise 27.2 | Q 1.4

If 4 cos² x° - 1 = 0 and 0 ∠ x° ∠ 90°,
find:(i) x°
(ii) sin² x° + cos² x°
(iii) `(1)/(cos^2xx°) – (tan^2 xx°)`

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

Solve for x : tan² (x - 5°) = 3

Solve for x : cos² 30° + cos² x = 1

If θ = 30°, verify that: tan2θ = `(2tanθ)/(1 - tan^2θ)`

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: `(sec34°)/("cosec"56°)`

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

If A + B = 90°, prove that `(tan"A" tan"B" + tan"A" cot"B")/(sin"A" sec"B") - (sin^2"B")/(cos^2"A")` = tan²A