The Hidden Partner Expression

Introduction to Trigonometry

The Hidden Partner Expression

CBSE Class 10 · Solve it one decision at a time. A wrong pick earns a nudge, never the answer.

Step 1 of 4

The problem

If 5sin⁡θ+12cos⁡θ=13,5\sin\theta + 12\cos\theta = 13, prove that tan⁡θ=512.\tan\theta = \dfrac{5}{12}.

Step 1 · Your move

Expand (5sin⁡θ+12cos⁡θ)2+(12sin⁡θ−5cos⁡θ)2(5\sin\theta + 12\cos\theta)^2 + (12\sin\theta - 5\cos\theta)^2. What happens to the sin⁡θcos⁡θ\sin\theta\cos\theta terms?

5sin⁡θ+12cos⁡θ=135\sin\theta + 12\cos\theta = 13
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