Question

Cosec x - cot x = 3/2,find cos x

Answer 1

Step-by-step explanation:

cosec x - cot x =3/2. ......(1)

we know that cosec^2 x-cot^2 x=1

(cosec x+cot x)(cosec x - cot x)=1.

put value of cosec x - cot x=3/2.

so..

( cosec x+ cot x)(3/2)=1.

cosec x + cot x=2/3. ....(2).

eq^n (1)+ eq^2 (2).......

so .....

2 cosec x = 13/6.

cosec x= 13/12.

and ...

sin x = 12/13.

put value of cosec x.... in (1).

so...

13/12-cot x= 3/2.

13/12-3/2=cot x.

(13-18)/12=cot x.

-5/12= cot x.

or

cot x= -5/12.

but we know that.. cos x= √(1-sin^2 x)

=√{1-(12/13)^2}

=√{1-144/169}

=√{25/169}.

=5/13.

I hope it's right and helps u.

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