Question

1/cotA+tanA= find the value
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Answer 1

Answer:

$\dfrac{1}{cotA + tanA}$

$\implies \dfrac{1}{\dfrac{1}{tanA} + tanA}$

$\implies \dfrac{1}{\dfrac{1+ tan^2A}{tanA}}$

$\implies \dfrac{tanA}{1+tan^2A}$

$\implies \dfrac{tanA}{sec^2A}$

$\implies \dfrac{sinA}{cosA} \times cos^2A$

$\implies {sinAcosA}$

$\implies \dfrac{sin2A}{2}$

Identities used :

1️⃣ $cotA = \dfrac{1}{tanA}$

2️⃣ $1 + tan^A = sec^A$

3️⃣ $tanA = \dfrac{sinA}{cosA}$

4️⃣ $secA = \dfrac{1}{cosA}$

5️⃣ $2sinAcosA = sin2A$

Additional information :

$\begin{lgathered}</p><p>\boxed{\begin{array}{l}</p><p>\sf Fundamental \ trigonometric\ identities:\\ \\</p><p>\rm sin^2\theta + cos^2\theta = 1\\</p><p>\rm 1 + tan^2 \theta = sec^2 \theta\\</p><p>\rm 1 + cot^2\theta = cosec^2\theta \\</p><p>\end{array}}\end{lgathered}$