Question

If sin + cos = root3 Prove that tan + cot = 1

Answer 1

Hey mate

$\sin( \alpha ) + \cos( \alpha ) = \sqrt{3}$

On squaring both sides

${sin}^{2} ( \alpha ) + \cos {}^{2} ({ \alpha } ) + 2 \sin( \alpha ) . \cos( \alpha ) = 3$

$2 \sin( \alpha ) . \cos( \alpha ) = 3 - 1 = 2$

Now we get

$\sin( \alpha ) . \cos( \alpha ) = 1$

Now, Taking RHS

$\tan( \alpha ) + \cot( \alpha )$

writing it's extended form

sin^2+cos^2/cos.sin=1

So we get

tan+cot=1

HENCE PROVED

Answer 2

SOLUTION

Given,

sin + cos = √3

sin + cos = √3 Prove = tan + cot =1

(sin + cos)^2= 3

=)sin^2 + cos^2 + 2 sin.cos = 3

=) 1+ 2 sin.cos= 3

=) 2sin.cos = 2

=) sin.cos= 1............(1)

=) tan + cot = sin/cos+ cos/sin

=)tan + cot = sin^2+ cos^2/sin.cos

=) tan+ cot = 1/sin.cos= 1/1 {sin.cos= 1 from (1)

=) tan + cot = 1

hence, proved

hope it helps ✔️