Question

Prove that
tan75°+cot75°=4​

Answer 1

Hlew,

Here's your answer...

tan75°=tan(30°+45°)

=(tan30°+tan45°)/(1-tan30°tan45°)

={(1/√3)+1}/{1-(1/√3)(1)}

=(√3+1)/(√3-1)

So,cot75°=1/tan75°

=(√3-1)/(√3+1)

Then,tan75°+cot75°={(√3+1)2+(√3-1)2}/{(√3)2-(1)2}

=(3+1+2√3+3+1-2√3)/(3-1)

=4.

Thanks.

Sorry baby 'wink'

Answer 2

Bonjour❤

Step-by-step explanation:

tan75°=tan(30°+45°)

=(tan30°+tan45°)/(1-tan30°tan45°)

={(1/√3)+1}/{1-(1/√3)(1)}

=(√3+1)/(√3-1)

=»cot75°=1/tan75°

=(√3-1)/(√3+1)

tan75°+cot75°={(√3+1)2+(√3-1)2}/{(√3)2-(1)2}

=(3+1+2√3+3+1-2√3)/(3-1)

=4.