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1. Verify \(cos \ 3A = 4 cos^3 \ A - 3 cos \ A\), when \(A = 30^{\circ}\).
Proof:
LHS: \(cos \ 3A =\)
RHS: \(4 cos^3 \ A - 3 cos \ A =\)
Since LHS \(=\) RHS, \(cos \ 3A = 4 cos^3 \ A - 3 cos \ A\), when \(A = 30^{\circ}\).
Hence, we proved.
2. Find the value of \(8 sin \ 2x \ cos \ 4x \ sin \ 6x\), when \(x = 15^{\circ}\).
Answer:
\(8 sin \ 2x \ cos \ 4x \ sin \ 6x =\)
3. Verify \(sin^2 \ 60^{\circ} + cos^2 \ 60^{\circ} = 1\).
Proof:
\(sin^2 \ 60^{\circ} =\)
\(cos^2 \ 60^{\circ} =\)
\(sin^2 \ 60^{\circ} + cos^2 \ 60^{\circ} =\)
Since LHS \(=\) RHS, then \(sin^2 \ 60^{\circ} + cos^2 \ 60^{\circ} = 1\).
Hence, we proved.
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