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प्रश्न
Find the value of:
`4 (sin^2 30° + cos^2 60°) − 3 (cos^2 45° − 1/2 sin^2 90°)`
बेरीज
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उत्तर
Given:
`4 (sin^2 30° + cos^2 60°) − 3 (cos^2 45° − 1/2 sin^2 90°)`
Step 1: Use standard trigonometric values
sin 30° = `1/2 → sin^2 30° = 1/4`
cos 60° = `1/2 → cos^2 60° = 1/4`
cos 45° = `1/sqrt2 → cos^2 45° = 1/2`
sin 90° = 1 → `sin^2 90° = 1`
Step 2: Substitute the values
`4(1/4 + 1/4) = 4 ⋅ 2/4 = 4 ⋅ 1/2 = 2`
`3(1/2 − 1/2 ⋅ 1) = 3 (1/2 − 1/2) = 3(0) = 0`
= 2 − 0 ...[Subtracting]
= 2
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