Question for Practice on Trigonometry

Question of The Day24-08-2020

What will be the value of (1 – cot 23⁰) (cot 22⁰ – 1)?

Answer

Correct Answer : b ) \(– 2\)

Explanation :

Consider A + B = 45⁰

Taking cot on both the sides

cot (A + B) = cot 45⁰

\(\frac {cotAcotB-1 }{cotA+cotB}=1\)

cot A cot B – 1 = cot A + cot B

cot A cot B – cot A – cot B = 1

Adding 1 on both the side

cot A cot B – cot A – cot B + 1 = 1 + 1

(cot A – 1) (cot B – 1) = 2

So, when A + B = 45⁰, then (cot A – 1) (cot B – 1) = 2

According to the question,

Let A = 23⁰ and B = 22⁰

A + B = 45⁰

So, (cot 23⁰ – 1) (cot 22⁰ – 1) = 2

And, (1 – cot 23⁰) (cot 22⁰ – 1) = – 2

Hence, (b) is the correct answer.

Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA, UP SI etc.

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