Question

If cosec theta +cot theta=k, then prove that cos theta =
K²-1÷
k²+1​

Answer 1

Given,

cosece + cot0 = k

cos0

= k

sine

1

sin0

1+cos0

= k

sine

1+ cose =

ksine

Squaring both side,

(1+cos0)² = k²sin²0

(1+ cos0)² = k²(1 – cos?0)

(1+ cos0).(1+cos0) = k²(1+ cos0)(1 –

cos0)

1+ cos0 = k²(1 – cos0)

1+ cos0 = k² – k²cos0

1+(1+k²)cos0 = k?

(1+k²)cos0 = k² – 1

cosθ= k 2 +1k 2−1