Question

if sin teta - cos teta=1/2, then find the value of 1/sin teta + cos teta.

Answer 1

Answer of the above question is √7/2.

Answer 2

Hi Mate!!

Let, theta = x

Sin ( x ) - Cos ( x ) = 1 / 2

Squaring both sides we have

{ Sin ( x ) - Cos ( x ) }²= { 1 / 2 }²

=>

Sin² ( x ) + Cos² ( x ) - 2 Sin ( x ) Cos ( x ) = 1 / 4

=>

1 - 2 Sin ( x ) Cos ( x ) = 1 / 4

1 - ( 1 / 4 ) = 2 Sin ( x ) Cos ( x )

Sin ( x ) Cos ( x ) = 3 / 8

Sin ( x ) + Cos ( x ) / 2 ≥ { Sin ( x ) Cos ( x ) }½

Sin ( x ) + Cos ( x ) / 2 ≥ ( 3 / 8 )½

Sin ( x ) + Cos ( x ) ≥ 2 ( √3 ) / 2√2

Sin ( x ) + Cos ( x ) = √3 / √2

So , 1 / Sin ( x ) + Cos ( x ) = 1 / ( √3 / √2 )

1 / Sin ( x ) + Cos ( x ) = √2 / √3

Have a nice time...

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Formula used is

Sin² ( x ) + Cos² ( x ) = 1

And

A.M ≥ G . M