Question

prove that one upon sec theta + 10 theta minus one upon cos theta is equals to one upon cos theta minus one upon sec theta minus 10 theta

Answer 1

Step-by-step explanation:

1/( sec + tan ) - 1/ cos =

1/ [ ( 1/cos ) + (sin / cos ) ] - 1/cos

1/ [ (1+sin) / cos) ] - 1/cos

cos / ( 1+sin) - 1/cos

cos ^2 - (1+sin) / (1+sin) cos

1-sin^2 -1 -sin / (1+sin) cos

-sin ( sin +1) / (1+sin ) cos

= - tan

now taking rhs

1/ cos - 1/( sec - tan )

1/ cos - 1/ [ ( 1/cos) - ( sin /cos) ]

1/cos - 1/[ (1-sin ) / cos ]

1/ cos - cos / (1-sin)

(1-sin - cos ^2 )/ [cos ( 1-sin) ]

[1-sin - ( 1 - sin^2) ]/ [cos( 1- sin ) ]

( 1-sin -1 + sin ^2 ) / cos ( 1-sin)

- sin ( 1-sin ) / cos ( 1-sin )

- sin / cos

- tan

LHS = rhs