Find the value of tan(-135º) and cot(-135º) along with the steps.

Solution:

We can approach this question in multiple ways by using trigonometric tables.

Using the property that reciprocal of a tangent function is nothing but a cotangent function itself.

tan (-135º) = tan (360º - 135º)

= tan (225º)

= tan (180º + 45º)

= {tan (180º) + tan (45º)} / { 1 - tan (180º) tan (45º)}

= (0 + 1) / (1 - 0)

= 1

135 is in 2^nd quadrant. Tan is negative. Thus tan 135 = -1

Since, tan (-x) = 1/cot (-x)

therefore, cot (-135º) = 1/tan (-135º)

= 1/-1

= -1

cot 135 = -1

Hence, the value of both tan (-135º) and cot (-135º) is equal to -1.

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Find the value of tan(-135º) and cot(-135º) along with the steps.

Summary:

The value of both tan(-135º) and cot(-135º) is equal to 1.