Question

1/tan + 1/cot=1/sin×cos​

Answer 1

Answer:

True

Step-by-step explanation:

Input:

1/tan(θ) + 1/cot(θ) = 1/(sin(θ) cos(θ))

Result:

True

Answer 2

Formulas used:-

$\longrightarrow$$\underline\red{\boxed{\bf CotØ = \dfrac{1}{TanØ}}}$

$\longrightarrow$$\underline\green{\boxed{\bf CotØ = \dfrac{CosØ}{SinØ}}}$

$\longrightarrow$$\underline\orange{\boxed{\bf TanØ = \dfrac{SinØ}{CosØ}}}$

$\longrightarrow$$\underline\pink{\boxed{\bf Sin²Ø+Cos²Ø = 1}}$

Solution

:$\implies$$\sf\dfrac{1}{TanØ}$ + $\sf\dfrac{1}{CotØ}$

:$\implies$$\sf\dfrac{CotØ+TanØ}{TanØ.CotØ}$

:$\implies$$\sf\dfrac{CotØ+TanØ}{TanØ×\dfrac{1}{TanØ}}$

:$\implies$$\sf\dfrac{CotØ+TanØ}{1}$

:$\implies$$\sf\dfrac{CosØ}{SinØ}+\dfrac{SinØ}{CosØ}$

:$\implies$$\sf\dfrac{Cos²Ø+Sin²Ø}{SinØ.CosØ}$

:$\implies$$\sf\dfrac{1}{SinØ.CosØ}$ = R.H.S

hence verified