If 0 < A < 90^ , then the value of 1/2 A [ 1 + ( sec A - tan A ) cose… — Trigonometry MCQ

Aptitude · Q146

Trigonometry

Competitive Exams · Aptitude · question 146

Q146

If

0 < A < 9 0^{\circ},

then the value of

\frac{1}{2} cot A

[\frac{1 + ( secA - tan A )}{cosecA ( sec A - tan A )}]

= ?

A.

0

B.

2

C.

1

Answer

D.

\frac{1}{2}

Answer: Option C

Solution

Answer: Option C

Solution:

According to the question, Put A = 4 5^{\circ} \Rightarrow \frac{1}{2} \times cot 4 5^{\circ} [\frac{1 + ( sec 45 ^{\circ} + tan 45 ^{\circ} )}{cosec 45 ^{\circ} ( sec 45 ^{\circ} - tan 45 ^{\circ} )}] \Rightarrow \frac{1}{2} [\frac{1 + ( 2 - 1 ) ^{2}}{2 \times ( 2 - 1 )}] \Rightarrow \frac{1}{2} [\frac{1 + 2 + 1 - 2 2}{2 - 2}] \Rightarrow \frac{1}{2} [\frac{4 - 2 2}{2 - 2}] \Rightarrow \frac{1}{2} \times 2 [\frac{2 - 2}{2 - 2}] \Rightarrow 1

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