Question

prove that sinA(1+tanA) + cosA(1+cotA) =secA+cosecA​

Answer 1

Answer:

Pls mark as brainliest

Thumbs up!!!!!!

sin(1+sin/cos)+cos(1+cos/sin)

sin(cos+sin/cos)+cos(sin+cos/sin)

(sin+cos)(sin/cos+cos/sin)

(sin+cos)/(sincos)

1/cos+1/sin

sec+cosec

Answer 2

$sin\ A(1+tan\ A) + cos\ A(1+cot\ A) = sec\ A + cosec\ A$

Solution:

Given that, we have to prove:

$sin\ A(1+tan\ A) + cos\ A(1+cot\ A) = sec\ A + cosec\ A$

Take LHS

$sin\ A(1+tan\ A) + cos\ A(1+cot\ A) \\\\sin\ A(1 + \frac{sin\ A}{cos\ A}) + cos\ A(1+ \frac{cos\ A}{sin\ A})\\\\ \frac{sin\ A}{cos\ A} ( sin\ A + cos\ A) + \frac{cos\ A}{sin\ A} (sin\ A + cos\ A)\\\\( sin\ A + cos\ A) [ \frac{sin\ A}{cos\ A}+ \frac{cos\ A}{sin\ A}]\\\\( sin\ A + cos\ A) [ \frac{sin^2 A+ cos^2 A}{sinA\ cos\ A}]$

$( sin\ A + cos\ A) [ \frac{1}{sinA\ cos\ A}]\\\\\frac{sin\ A}{sin\ A\ cos\ A} + \frac{cos\ A}{sin\ A\ cos\ A}\\\\\frac{1}{cos\ A} + \frac{1}{sin\ A}\\\\sec\ A + cosec\ A\\\\Thus$

$LHS = RHS\\\\THUS\ PROVED$

Learn more:

Prove that sina-2 sin^3a/2 cos^3a-cosa=tana

https://brainly.in/question/3116053

Prove that sinA- sin^3A/ 2cos^3 A- cos A = tanA

https://brainly.in/question/3134294