1.

If "cosec"theta+cottheta=c, then what is costheta equal to ?

Answer»

`(c)/(c^(2)+1)`
`(c)/(c^(2)-1)`
`(c^(2)-1)/(c^(2)+1)`
None of the above

Solution :Let`"COSEC "theta+cottheta=c`
`RARR(1)/(SINTHETA)+(costheta)/(sintheta)=crArr(1+costheta)/(sintheta)=c`
`rArr(1+(2" cos"^(2)(theta)/(2)-1))/(2"SIN"(theta)/(2)"cos"(theta)/(2))=crArr(2" cos"^(2)(theta)/(2))/(2"sin"(theta)/(2)"cos"(theta)/(2))=c`
`rArr"cot"(theta)/(2)=crArrcostheta=(1-(1)/(c^(2)))/(1+(1)/(c^(2)))=(c^(2)-1)/(c^(2)+1)`
`(becausecostheta=(1-TAN^(2)((theta)/(2)))/(1+tan^(2)((theta)/(2))))`
`rArr"tan"(theta)/(2)=(1)/(c)`


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