Trignometry

Quantitative Aptitude ( CCS)

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(1 – tan A)² + (1 + tan A)² + (1 – cot A)² + (1 + cot A)² is equal to

sin² A.cos² A

sec² A.cosec² A

2sec² A.cosec² A

None of these

Explanation:

(1 – tan A)² + (1 + tan A)² + (1 – cot A)² + (1 + cot A)²
= 1 + tan² A – 2 tan A + 1 + tan² A + 2 tan A + 1 + cot² A – 2 cot A + 1 + cot² A + 2 cot A
= 1 + tan² A + 1 + tan² A + 1 + cot² A + 1 + cot² A
= sec² A + sec² A + cosec² A + cosec² A
[? 1 + tan² A = sec² A and 1 + cot² A = cosec² A ]
= 2 (sec² A + cosec² A)

By: Amit Kumar

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