CDS 2025 · PYQ · Trigonometric Identities · medium
What is (1 + cot α − cosec α)(1 + tan α + sec α) equal to?
Answer
The correct answer is C: 2. Expanding: Let A = 1 + cot α − cosec α and B = 1 + tan α + sec α. Multiply: 1·1 + 1·tan α + 1·sec α + cot α·1 + cot α·tan α + cot α·sec α − cosec α·1 − cosec α·tan α − cosec…
- A.1/2
- B.1
- C.2✓ Correct
- D.4
Expanding: Let A = 1 + cot α − cosec α and B = 1 + tan α + sec α. Multiply: 1·1 + 1·tan α + 1·sec α + cot α·1 + cot α·tan α + cot α·sec α − cosec α·1 − cosec α·tan α − cosec α·sec α. Simplifying using cot α·tan α = 1 and grouping: this is a standard identity equal to 2.
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