Question

tan Q /1-cotQ+cotQ/1-tanQ =1+secQcosecQ

Answer 1

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LET Q=THETA



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Answer 2

This is a trigonometric identity involving tangent, cotangent, cosecant and secant.

The identity states that the ratio of tangent of Q over 1 minus cotangent of Q plus the ratio of cotangent of Q over 1 minus tangent of Q is equal to 1 plus secant of Q multiplied by cosecant of Q.

We can simplify this identity by using the reciprocal relationship between trigonometric functions.

cotangent of Q = 1/tan Q

cosecant of Q = 1/sin Q

secant of Q = 1/cos Q

By substituting these values in the identity we get:

tanQ/(1-1/tanQ) + (1/tanQ)/(1-tanQ) = 1+(1/cosQ)(1/sinQ)

This simplifies to:

tanQ + cotQ = 1 + cosecQ secQ

This identity can be used to simplify trigonometric expressions involving tangent, cotangent, cosecant, and secant.

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