UPSKILL MATH PLUS

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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:
 
\(sin^2 \ 60^{\circ} =\) ii
 
\(cos^2 \ 60^{\circ} =\) ii
 
\(sin^2 \ 60^{\circ} + cos^2 \ 60^{\circ} =\)
 
Since LHS \(=\) RHS, then \(sin^2 \ 60^{\circ} + cos^2 \ 60^{\circ} = 1\).
 
Hence, we proved.