Question

Given A is an acute angle and cosec A = √2, find the value of-

2 sin^2 A + 3 cot^2 A / tan^2 A - cos^2 A ​

Answer 1

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Answer 2

Given:

A=√2

So,AC/BC=√2/1

AC=BC√2

Then,

BC=x

In ∆ABC,

By Pythagorean theorem,

(AC)^2=(AB)^2+(BC)^2

(√2x)^2=(AB)^2+(x)^2

AB=x

${\boxed{\blue{\bf{SIN A=PERPENDICULAR /HYPOTENUSE}}}}$=BC/AC=1/√2

${\boxed{\green{\bf{COT A=BASE /HYPOTENUSE}}}}$=X/X=1

${\boxed{\blue{\bf{TAN A=PERPENDICULAR /BASE}}}}$=X/X=1

${\boxed{\green{\bf{COS A=BASE/HYPOTENUSE}}}}$=X/√2=1/√2

Substituting the values,

2 sin^2A+3 COT^2 A/(TAN^2 A- COS^2 A)=8