Question

Prove that tan 45+cot75=4​

Answer 1

Answer:

tan(A+B)=tanA+tanB1−tanA×tanB

And

cotA=1tanA

So

tan75°

=tan(30°+45°)

=tan30°+tan45°1−tan30°×tan45°

=1/√3+11–1/√3×1

=√3+1√3–1

And

cot75°=1/tan75°=√3−1√3+1

So

tan75°+cot75°

=√3+1√3–1+√3−1√3+1

=(√3+1)2+(√3–1)2(√3−1)(√3+1)

=(3+1+2√3)+(3+1−2√3)3−1

=3+1+3+12

=4

hope this have helped you out

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