Question

If sac theta + tan theta =x
express cosec ² in terms of x.​

Answer 1

Step-by-step explanation:

We have,

secθ+tanθ=x ……. (1)

(secθ−tanθ)

(secθ+tanθ)(secθ−tanθ)

=x

(secθ−tanθ)

(sec

2

θ−tan

2

θ)

=x

We know that

sec

2

θ−tan

2

θ=1

Therefore,

(secθ−tanθ)

1

=x

secθ−tanθ=

x

1

……. (2)

On adding the equation (1) and (2), we get

2secθ=x+

x

1

2secθ=

x

x

2

+1

secθ=

2x

x

2

+1