Question

Cosec2 30, sin2 45 - sec2 60= - 2

Answer 1

cosec2 30 sin2 45-sec2 60

Cosec²30Sin²45 -Sec^ 2 60

Cosec= matrix 1\\ Sin matrix \&Sec= matrix 1\\ Cos matrix

= matrix 1\\ Sin^ 2 30 matrix * Sin^ 2 45- matrix 1\\ Cos^ 2 60 matrix

Cos theta=Sin(90- theta) Rightarrow Cos60=?

= matrix 1\\ Sin^ 2 30 matrix * Sin^ 2 45- matrix 1\\ Sin^ 2 30 matrix

= matrix 1\\ Sin^ 2 30 matrix *(Sin^ 2 45-1)

Sin30= matrix 1\\ 2 matrix \&Sin45= matrix 1\\ sqrt 2 matrix

= matrix 1\\ ( 1 2 )^ 2 *(( 1 sqrt 2 )^ 2 -1)

=4*( 1 2 -1)

=4*(- 1 2 )

=-2

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