Question

If 7 square theta + 3 cos square theta is equal to 4 sin square theta + cos square theta then show that cot theta is equal to root 3 if 7 square theta + 3 cos square theta is equal to 4 sin square theta + cos square theta then show that cos theta is equal to 3

Answer 1

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Answer 2

Heya!

• 7 sin^2 theta + 3 cos^2 theta = 4
• 4 sin^2 theta + 3 sin^2 theta + 3 cos^2 theta = 4
• 4 sin^2 theta + 3 (sin^2 + cos^2) = 4
• 4 sin^2 theta + 3 (1) = 4
• 4 sin^2 theta = 4 - 3
• sin^2 theta = 1/4
• sin theta = 1/2
• Therefore, theta = 30 degree.
• tan 30 = 1 / root (3)  

Hence Proved.