What is the value of ?
Answer and explanation
Correct answer: A.
- Step 1: In a right triangle with legs and hypotenuse , $sin heta = dfrac{a}{c}$ and $cos heta = dfrac{b}{c}$.
- Step 2: Sum the squares: . By the Pythagorean theorem, , so the expression simplifies to .
Answer
.
Why not the others: Other options result from confusing reciprocal trigonometric ratios, applying incorrect complementary angle identities, or algebraic slips in squaring ratios.
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