Question

plz solve this plzzzzz​

Answer 1

GOOD MORNING!!!!

L.H.S

let theta = x

( Tanx + Sec x - 1 )
______________
( Tan x - Sec x + 1 )

MULTIPLY Numerator and DENOMINATOR by ( Tan x + Sec x - 1 )

we get

=>

{ Tan x + Sec x - 1 }²
________________
{ Tan x - Sec x + 1 } × { Tan x + Sec x - 1}

=>

Tan² x + ( sec x -1 )² + 2Tan x ( sec x -1 )
____________________
Tan²x - ( sec x - 1 )²

=>

Tan² x + Sec²x +1 -2sec x +2Tan x ( secx-1)
___________________
Tan² x - Sec² x - 1 + 2secx

=>

-1 + Sec²x + Sec² x + 1 - 2secx + 2Tanx(secx - 1 )
____________________
Sec²x -1 - Sec² x + 2secx -1

=>

2 secx { Sec x - 1 }+ 2Tanx ( sec x - 1)
___________________
2( Sec x - 1 )

=>

Tan x + Sec x

= (1 + Sinx) / Cosx

Formula used

1 + Tan² x = Sec² x

And

( a + b )² = a² + b² + 2ab

2)

Cos 2x = Cos ( 60 - 30 )

Cos 2x = Cos 30

2x = 30

So, sin ( 2x ) = Sin (30 ) = 1/2

Formula used

Cos ( A - B ) = Cos A × Cos B + SinA × SinB