Find the value of sin73° + cos137&de

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

Find the value of sin73° + cos137°

Options:

sin13°

cos13°

cos18°

sin18°

Correct Answer:

sin13°

Explanation:

sin73° + cos137° [(cos90°+θ) = -sinθ]

= sin73° + (-sin47°) [sin(c-d) = 2cos\(\frac{c+d}{2}\) × sin\(\frac{c - d}{2}\)]

⇒ 2cos(\(\frac{73+47}{2}\)) × sin(\(\frac{73 - 47}{2}\))

2 × cos60° × sin13°

2 × \(\frac{1}{2}\) × sin13°

= sin13°