The value of (sin30° + cos30°) – (sin60° + cos60° ) is
a. -1
b. 0
c. 1
d. 2

Solution:

We have to find the value of (sin30° + cos30°) - (sin60° + cos60°).

sin 30° = 1/2

cos 30°= √3/2

sin 60° = √3/2

cos 60° = 1/2

(sin 30° + cos 30°) = 1/2 + √3/2 = (1 + √3)/2

(sin 60° + cos 60°) = √3/2 + 1/2 = (√3 + 1)/2

(sin 30° + cos 30°) - (sin 60° + cos 60°) = ((1 + √3)/2) - ((√3 + 1)/2)

= 1/2 + √3/2 - √3/2 - 1/2

= 0

Therefore, the value of (sin 30° + cos 30°) - (sin 60° + cos 60°) is 0.

✦ Try This: The value of (sin60° + cos30°) + (sin 45° + cos 30° ) is

We have to find the value of (sin60° + cos30°) + (sin 45° + cos 30°)

Using the trigonometric identities,

cos 30°= √3/2

sin 60° = √3/2

sin 45° = √2/2

sin60° + cos30° = √3/2 + √3/2 = 2√3/2 = √3

sin 45° + cos 30° = √2/2 + √3/2 = (√2 + √3)/2

(sin60° + cos30°) + (sin 45° + cos 30°) = √3 + (√2 + √3)/2

Taking LCM

= (2√3 + √2 + √3)/2

= (3√3 + √2)/2

Therefore, (sin60° + cos30°) + (sin 45° + cos 30°) = (3√3 + √2)/2

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8

NCERT Exemplar Class 10 Maths Exercise 8.1 Sample Problem 1

The value of (sin30° + cos30°) – (sin60° + cos60° ) is a. -1, b. 0, c. 1, d. 2

Summary:

The value of (sin30° + cos30°) – (sin60° + cos60° ) is zero

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