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If sintheta1sintheta2-costheta1costheta2...

If `sintheta_1sintheta_2-costheta_1costheta_2+1=0,` then the value of `tan((theta_1)/2)cot((theta_2)/2)` is equal to `-1` (b) 1 (c) 2 (d) `-2`

A

`-1`

B

1

C

2

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
A
`sin theta_(1) sintheta_(2)=-1`
or `cos (theta_(1)+theta_(2))=1`
`rArr theta_(1)+theta_(2)=2npi, n in I`
or `(theta_(1))/(2)+(theta_(2))/(2)=npi`
Thus, `tan""(theta_(1))/(2)cot""(theta_(2))/(2)=tan""(theta_(1))/(2)cot(npi-(theta_(1))/(2))`
`=-tan""(theta_(1))/(2)cot""(theta_(1))/(2)=-1`
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