Question

If cosecA=√2 find the value of tan root 2 A-1.

Answer 1

Answer:

2

Step-by-step explanation:

cosecA = \sqrt{2}. Therefore, sinA=\frac{1}{\sqrt{2}}

A=45^0

cosA=cos45^0=\frac{1}{\sqrt{2}}

tanA=tan45^0=1

cotA=cot45^0=1

Therefore, 2sin^2A + 3cot^2A=2(\frac{1}{\sqrt{2} })^2+3(1)^2=4

4(tan^2 A-cos^2A)=4(1^2-(\frac{1}{\sqrt{2}})^2)=4(1-\frac{1}{2})=2

Hence, \frac{2sin^2A + 3cot^2 A}{4(tan^2 A - cos^2A)}=\frac{4}{2}=2

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