Question

Find the value of the
expression
cosec (58+theta) – Sec (32-theta)
tan 45 + tan (45+ theta) - cot (45-theta)​

Answer 1

The value of the expression=1

Step-by-step explanation:

$cosec (58+\theta)-sec(32-\theta)+tan 45+tan (45+\theta)-cot(45-\theta)$

The expression can be written as

$Cosec (90-(32-\theta))-sec(32-\theta)+tan 45+tan(90-(45-\theta))-cot(45-\theta)$

We know that

$cosec(90-\theta)=sec\theta$

$tan(90-\theta)=cot\theta$

Using the formula then we get

$sec(32-\theta)-sec(32-\theta)+tan45+cot(45-\theta)-cot(45-\theta)$

$tan 45$

We know that

$tan 45=1$

Using the value then we get

$tan 45=1$

The value of given expression=1

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