Question

SinA = CosA ,0<A<90, then tanA + cotA =

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Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

$\rm :\longmapsto\:sinA = cosA$

Consider,

$\rm :\longmapsto\:tanA + cotA$

$\rm \: = \:\dfrac{sinA}{cosA} + \dfrac{cosA}{sinA}$

$\rm \: = \:\dfrac{ {sin}^{2}A + {cos}^{2}A}{sinAcosA}$

can be rewritten as

$\rm \: = \:\dfrac{ {sin}^{2}A + {sin}^{2}A}{sinA \times sinA}$

$\rm \: = \:\dfrac{2 {sin}^{2} A}{ {sin}^{2} A}$

$\rm \: = \:2$

$\bf\implies \:\boxed{ \tt{ \: tanA + cotA = 2}}$

Alternative Method : 02

Given that,

$\rm :\longmapsto\:sinA = cosA$

can be rewritten as

$\rm :\longmapsto\:\dfrac{sinA}{cosA} = 1$

$\bf\implies \:tanA = 1$

Now, Consider

$\rm :\longmapsto\:tanA + cotA$

$\rm \: = \:tanA + \dfrac{1}{tanA}$

$\rm \: = \:1 + 1$

$\rm \: = \:2$

Hence,

$\bf\implies \:\boxed{ \tt{ \: tanA + cotA = 2}}$

Alternative Method :- 03

Given that,

$\rm :\longmapsto\:sinA = cosA$

can be rewritten as

$\rm :\longmapsto\:\dfrac{sinA}{cosA} = 1$

$\rm :\longmapsto\:tanA = 1$

$\rm :\longmapsto\:tanA = tan45 \degree$

$\bf\implies \:A = 45 \degree$

Now, Consider

$\rm :\longmapsto\:tanA + cotA$

$\rm \: = \:tan 45 \degree + cot 45 \degree$

$\rm \: = \:1 + 1$

$\rm \: = \:2$

Hence,

$\bf\implies \:\boxed{ \tt{ \: tanA + cotA = 2}}$

Answer 2

Answer:

$\large\underline{\sf{Solution-}}$

Given that,

$\rm :\longmapsto\:sinA = cosA$

Consider,

$\rm :\longmapsto\:tanA + cotA$

$\rm \: = \:\dfrac{sinA}{cosA} + \dfrac{cosA}{sinA}$

$\rm \: = \:\dfrac{ {sin}^{2}A + {cos}^{2}A}{sinAcosA}$

can be rewritten as

$\rm \: = \:\dfrac{ {sin}^{2}A + {sin}^{2}A}{sinA \times sinA}$

$\rm \: = \:\dfrac{2 {sin}^{2} A}{ {sin}^{2} A}$

$\rm \: = \:2$

$\bf\implies \:\boxed{ \tt{ \: tanA + cotA = 2}}$

Alternative Method : 02

Given that,

$\rm :\longmapsto\:sinA = cosA$

can be rewritten as

$\rm :\longmapsto\:\dfrac{sinA}{cosA} = 1$

$\bf\implies \:tanA = 1$

Now, Consider

$\rm :\longmapsto\:tanA + cotA$

$\rm \: = \:tanA + \dfrac{1}{tanA}$

$\rm \: = \:1 + 1$

$\rm \: = \:2$

Hence,

$\bf\implies \:\boxed{ \tt{ \: tanA + cotA = 2}}$

Alternative Method :- 03

Given that,

$\rm :\longmapsto\:sinA = cosA$

can be rewritten as

$\rm :\longmapsto\:\dfrac{sinA}{cosA} = 1$

$\rm :\longmapsto\:tanA = 1$

$\rm :\longmapsto\:tanA = tan45 \degree$

$\bf\implies \:A = 45 \degree$

Now, Consider

$\rm :\longmapsto\:tanA + cotA$

$\rm \: = \:tan 45 \degree + cot 45 \degree$

$\rm \: = \:1 + 1$

$\rm \: = \:2$

Hence,

$\bf\implies \:\boxed{ \tt{ \: tanA + cotA = 2}}$