Exams › SSC CGL (Prelims) › General

If cos theta = 3/5, evaluate (2 sin theta + 5 cos theta)^2 + (5 sin theta - 2 cos theta)^2.

1. 29
2. 19
3. 39
4. 49

Correct answer: 29

Solution

Expanding gives 4sin^2 + 20 sin cos + 25 cos^2 + 25 sin^2 - 20 sin cos + 4 cos^2. The cross terms cancel, leaving 29 sin^2 + 29 cos^2 = 29.

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