Question

If tan A=cot B ,prove that A+B =90degree.​

Answer 1

Answer:

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Step-by-step explanation:

    tan A = cot B ------------ ( eq. i)   { given }

also, tan A = cot ( 90 - A ) ------------ ( eq.ii )   { complimentary angle }

From eq. i & ii -

  cot B = cot ( 90°- A )

⇒ B = 90° - A.

⇒ 90 ° = A + B.

⇒ A + B = 90 °. [ PROVED ] .

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Answer 2

Given, tan A=cot B

Now,

$tanA=\frac{1}{tanB} \\tan A*tan B=1\\\because A=45^{\circ}, B=45^{\circ}$

Where, A and B lies 0 to 90 degrees.

$\because A=B=45^{\circ}\\\therefore A+B=90^{\circ}$

...Hence Proved

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