Given that sinα = 1/2 and cosβ = 1/2, then the value of (α + β) is
a. 0°
b. 30°
c. 60°
d. 90°
Solution:
Given, sinα = 1/2 and cosβ = 1/2
We have to find the value of (α + β)
Using the trigonometric ratios of angles,
Given, sinα = 1/2
α = sin⁻¹(1/2)
α = 30°
Given, cosβ = 1/2
β = cos⁻¹(1/2)
β = 60°
Now, (α + β) = 30° + 60°
= 90°
Therefore, the value of (α + β) = 90°
✦ Try This: Given that sinA = 1/√2 and cosB = 1/2, then the value of (A + B) is
Given, sinA = 1/√2 and cosB = 1/2
We have to find the value of (A + B)
A = sin⁻¹(1/√2)
Using the trigonometric ratio of angles,
sin 45° = 1/√2
A = 45°
B = cos⁻¹(1/2)
Using the trigonometric ratio of angles,
cos 60° = 1/2
B = 60°
Now, (A + B) = 45°+60° = 105°
Therefore, the value of (A + B) = 105°
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.1 Problem 10
Given that sinα = 1/2 and cosβ = 1/2, then the value of (α + β) is a. 0°, b. 30°, c. 60°, d. 90°
Summary:
Given that sinα = 1/2 and cosβ = 1/2, then the value of (α + β) is 90°
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