SSC (English Medium) Class 10th Board ExamMaharashtra State Board
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# Prove that sin^6θ + cos^6θ = 1 – 3 sin^2θ. cos^2θ. - SSC (English Medium) Class 10th Board Exam - Geometry

#### Question

Prove that sin6θ + cos6θ = 1 – 3 sin2θ. cos2θ.

#### Solution

LHS = sin6θ + cos6θ

= (sin2θ)3 + (cos2θ)3

= (sin2θ + cos2θ) (sin4θ + cos4θ - sin2θ⋅cos2θ)

= (1)[(sin2θ + cos2θ)2 - 2sin2θ⋅cos2θ - sin2θ⋅cos2θ]

= (1)[(1)2 - 3sin2θ⋅cos2θ]

= 1 - 3sin2θ ⋅ cos2θ

= RHS

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#### APPEARS IN

2014-2015 (March) (with solutions)
Question 4.2 | 4.00 marks

#### Video TutorialsVIEW ALL [5]

Solution Prove that sin^6θ + cos^6θ = 1 – 3 sin^2θ. cos^2θ. Concept: Trigonometric Identities.
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