Prove the following: sin230° + cos230° = 1 2 sec 60 °

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

Sum

L.H.S.

= sin²30° + cos²30°

= `(1/2)^2 + (sqrt(3)/2)^2`

= `(1)/(4) + (3)/(4)`

= `(4)/(4)`
= 1

= `(1)/(2) xx sec60°`
= R.H.S.

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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 14.4

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°)`

State for any acute angle θ whether tan θ increases or decreases as θ decreases.

Find the value of 'A', if cot 3A = 1

If tanθ= cotθ and 0°≤ θ ≤ 90°, find the value of 'θ'.

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

Find the value of: `sqrt((1 - sin^2 60°)/(1 + sin^2 60°)` If 3 tan²θ - 1 = 0, find the value
a. cosθ
b. sinθ

In right-angled triangle ABC; ∠B = 90°. Find the magnitude of angle A, if:
a. AB is `sqrt(3)` times of BC.
B. BC is `sqrt(3)` times of BC.

Evaluate the following: `(sec32° cot26°)/(tan64° "cosec"58°)`

Evaluate the following: sin35° sin45° sec55° sec45°

Evaluate the following: cos39° cos48° cos60° cosec42° cosec51°