Question

Expression 2 cos2α – 1 can be simplified to

Answer 1

Answer:

sin2α=1−cos2αsin2⁡α=1−cos2⁡α

and express everything in terms of cos2αcos2⁡α:

R=(sin2α)3+(cos2α)3+K((sin2α)2+(cos2α)2)=(1−cos2α)3+(cos2α)3+K((1−cos2α)2+(cos

Answer 2

To Find :- Expression (2•cos²α – 1) can be simplified ?

Solution :-

→ 2•cos²α – 1

putting 1 = sin²α + cos²α we get,

→ 2•cos²α - (sin²α + cos²α)

→ 2•cos²α - sin²α - cos²α

→ 2•cos²α - cos²α - sin²α

→ cos²α - sin²α

→ cosα × cosα - sinα × sinα

using cosA × cosB - sinA × sinB = cos(A + B) and taking A = α , B = α we get,

→ cos(α + α)

→ cos2α

hence, (2•cos²α – 1) can be simplified to cos2α .

Extra knowledge :- Double angle formulas :-

→ Sin 2A = 2•sin A•cos A

→ cos 2A = 2•cos²A - 1 = 1 - 2•sin²A = cos²A - sin²A

→ Tan 2A = (2•tan A) / (1 - tan²A)

Learn more :-

It sino + tano = m

tano - sino an

Then express the

values of m²-n² in terms

of M and N

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tanA/(1-cotA) + cotA/(1-tanA)

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