Question

tan teta in terms of coswc theta

Answer 1

Answer:

Tan Theta = Sin Theta / Cos Theta   ... ( 1 )

Cosec Theta = 1 / Sin Theta

=> Sin Theta = 1 / Cosec Theta   ...( 2 )

Substituting ( 2 ) in ( 1 ), we get

=> Tan Theta = ( 1 / Cosec Theta ) / Cos Theta

=> Tan Theta = 1 / Cosec Theta . Cos Theta

Or this can even be written as,

Tan Theta = Sec Theta / Cosec Theta     [ ∵ 1 / Cos Theta = Sec Theta ]

This is the required answer !

Answer 2

That's so easy

We know that tan theta is equal to sin theta / cos theta

So tan theta = sin theta / cos theta...(1)

And sin theta is equal to 1/cosec theta and cos theta is equal to 1/sec theta

So, sin theta = 1/cosec theta ............(2) And 1/cos theta = sec theta ...............(3)

From (1)

Tan theta = sin theta / cos theta

By putting the value of sin theta and 1/cos theta from (2) and (3)

Therefore, tan theta is equal = sec theta / cosec theta

Tan theta = sec theta / cosec theta