Question

if sin theta=a then find value of cot theta and sec theta

for ∆ABC prove that tanA + C/2 = cot B/2​

Answer 1

Answer:

Given sin theta = a

Step-by-step explanation:

NOW,

sin theta = √1-cos²theta

Or,

cos theta = √1- sin²theta

Or,

sec theta =√1/1-sin²theta

so,

sec theta= √1/1- a²

Also,

tan theta = √sec²theta - 1

Or,

tan theta = √a²/ 1- a²

Or,

cot theta = √1- a²/a²

                                      OR

tan A =cot (90 - A)                        ----------------------1.

In Triangle ABC;

Using angle sum property we get;

A + B + C = 180

Or,

A + C = 180 - B                       ---------------------------2.

given  ;

Tan (A + C/2)

Using 2. we get

tan (90 - B/2)

Or,

by 1. we get ;

cot (B/2) = LHS = RHS

Hence proved  ..

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