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Evaluate 4(Sin^2 30 + Cos^4 60^@) - 2/3 3[(Sqrt(3/2))^2 . [1/Sqrt2]^2] + 1/4 (Sqrt3)^2 - CBSE Class 10 - Mathematics

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Question

Evaluate: `4(sin^2 30 + cos^4 60^@) - 2/3 3[(sqrt(3/2))^2 . [1/sqrt2]^2] + 1/4 (sqrt3)^2`

Solution

`sin 30^@ = 1/2, cos 60 = 1/2, sin 60^@ = sqrt3/2, cos 45^@ = 1/sqrt2, tan 60^@ = sqrt3`

`=> 4[[1/2]^4 + [1/2]^4] - 2/3[(sqrt3/2)^2 - (1/sqrt2)^2] + 1/2 (sqrt3)^2`

`4[2. 1/16] - 2/3 [3/4 - 1/2] + 3/2`

`= 1/2  - 2/3 . 1/4  + 3/2 = 11/6`

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Solution Evaluate 4(Sin^2 30 + Cos^4 60^@) - 2/3 3[(Sqrt(3/2))^2 . [1/Sqrt2]^2] + 1/4 (Sqrt3)^2 Concept: Trigonometric Ratios of Some Specific Angles.
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