Question

(iv) Prove that
(sinA+ cosA)(tanA+ cotA)= secA + cosecA

Answer 1

Answer:

Step-by-step explanation:

We know that,tan A= sin A/cos A

                       and

                       cot A= cos A/sin A

(sin A+ cos A)(tan A+ cot A)

=(sin A+cos A)         {(sin A/cos A)    + (cos A/sin A)}

Taking LCM, we have

=(sin A+cos A) { $sin ^{2}A + cos ^{2} A$  /sin A cos A}

=(sin A+cos A) {1/sin A cos A)                           (  $sin ^{2}A + cos ^{2} A$)

=(sin A/sin A cos A) + (cos A/ sin A cos A)         (Cancelling common terms)

=1/cos A + 1/sin A

=sec A + cosec A