The expression(tan A/1-cot A)+(cot A/1-tan A) can be written as

Question

The expression(tan A/1-cot A)+(cot A/1-tan A) can be written as (A) sin A cos A +1 (B) secA cosecA + 1 (C) tanA + cotA (D) secA + cosecA

Tardigrade Admin · Accepted Answer

Given expression is (tan A/1-cot A)+(cot A/1-tan A) =(sin A/cos A)×(sin A/sin A-cos A)+(cos A/sin A)×(cos A/cos A-sin A) =(1/sin A-cos A) Big (sin3 A-cos3 A/cos A sin A) Big =(sin2+sin A cos A+cos2 A/sin A cos A) =(1+sin A cos A/sin A cos A)=1+sec A cosec A

Q. The expression $\frac{t an A}{1 - co t A} + \frac{co t A}{1 - t an A}$ can be written as

$s in A cos A + 1$

$sec A cosec A + 1$

$t an A + co t A$

$sec A + cosec A$

Q. The expression1−cotAtanA​+1−tanAcotA​ can be written as

sinAcosA+1

secAcosecA+1

tanA+cotA

secA+cosecA

Given expression is 1−cotAtanA​+1−tanAcotA​ =cosAsinA​×sinA−cosAsinA​+sinAcosA​×cosA−sinAcosA​ =sinA−cosA1​{cosAsinAsin3A−cos3A​} =sinAcosAsin2+sinAcosA+cos2A​ =sinAcosA1+sinAcosA​=1+secAcosecA

Q. The expression $\frac{t an A}{1 - co t A} + \frac{co t A}{1 - t an A}$ can be written as

$s in A cos A + 1$

$sec A cosec A + 1$

$t an A + co t A$

$sec A + cosec A$