Question

Without using trigonometry evaluate
If 7 sin²Q+ 3 cos2Q=4, than show that tanQ=1/√3

Answer 1

Answer:-

Given:

7 sin² Q + 3 cos² Q = 4

We know that,

sin² A + cos² A = 1

→ sin² A = 1 - cos² A

Hence,

7 sin² Q + 3 cos² Q = 4

→ 7(1 - cos² Q) + 3 cos² Q = 4

→ 7 - 7 cos² Q + 3 cos² Q = 4

→ - 4 cos² Q = 4 - 7

→ - 4 cos² Q = - 3

→ cos² Q = - 3/- 4

→ cos² Q = 3/4

→ Cos Q = √(3/4)

→ Cos Q = √3/2

√3/2 can be written as cos 30°.

Hence,

→ Cos Q = Cos 30°

On comparing both sides we get,

→ Q = 30°

We have to prove:

tan Q = 1/√3

→ tan 30° = 1/√3

→ 1/√3 = 1/√3. (tan 30° = 1/√3)

→ LHS = RHS

Hence, Proved.

Answer 2

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