Question

If a+b=90 then prove that tana.tanb=1

Answer 1

Hey

Given :-

tan a . tan b = 1 ...... (1)

a + b = 90

b = 90 - a

sub b in eq (1)

= tan a . tan (90-a)

= tan a . cot a

= 1

Answer 2

If a+b=90 then tan a·tan b=1.

Step-by-step explanation:

Given: $a+b=90$.

To prove: $\tan a\cdot \tan b=1$

$a+b=90$

$a=90-b$

Taking LHS,

$LHS=\tan a\cdot \tan b$

Substitute $a=90-b$ in the above equation.

$LHS=\tan (90-b)\cdot \tan b$

$LHS=\cot b\cdot \tan b$             $[\because \tan (90-x)=\cot x, if 0<x<90]$

$LHS=\dfrac{1}{\tan b}\cdot \tan b$

$LHS=1$

$LHS=RHS$

Hence proved.

#Learn more

If xsin³∅ + y cos³ ∅ = sin∅ . Cos∅ and xsin∅ = ycos∅, prove that x² + y² = 1

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