Question

if cosec theta =√5 find the value of 2-sin^2theta - cos^2theta​

Answer 1

cosecΘ=5

cosecΘ=PH=5

Thus, H=5,P=1

Using Pythagoras Theorem, 

H2=P2+B2

(5)2=12+B2

5=1+B2

B=2

Now, 2−sin2Θ−cos2Θ

= 2−(HP)2−(HB)2

= 2−(51)2−(52)2

= 2−51−54

= 2−1

= 1