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Question
If A = 30°;
show that:
cos 2A = cos4 A - sin4 A
Solution
Given that A = 30°
LHS = cos 2A
= cos 2(30°)
= cos 60°
= `(1)/(2)`
RHS = `cos^4"A" – sin^4"A"`
= `cos^4 30° – sin^4 30° `
= `(sqrt3/2)^4 – (1/2)^4`
= `(9)/(16) – (1)/(16)`
= `(1)/(2)`
LHS = RHS
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