Question

(sin a +cosec a )square + (cos a + sec a)square = 5+ sec a square× cosec a square

Answer 1

Hi ,

****************************

We know the trigonometric formulas

1 ) sin² A + cos² A = 1

2 ) sinA cosecA = 1

3 ) cosAsecA = 1

4 ) cosecA = 1/sinA

5 ) SecA = 1/CosA

*******************

LHS = ( sinA+ cosecA)²+(CosA+secA)²

=Sin² A+cosec²A+2sinAcosecA

+ Cos² A + sec² A + 2cosAsecA

= (Sin²A+cos²A)+2+2+cosec²A+sec² A

= 1+4 + 1/sin² A + 1/cos² A

= 5 + ( cos² A + sin² A ) / sin² A cos² A

= 5 + 1/sin² A cos² A

= 5 + cosec² A sec² A

= RHS

I hope this helps you.

:)