Question

Tan a + cot a = Sec a cosec a

Answer 1

Answer:

$\red{ \small{\tan(a) + \cot(a) = \sec(a) \times \csc(a)}}$

• True

Step-by-step explanation:

Verify the following identity:

• tan(a) + cot(a) = sec(a) csc(a)

Write

• cotangent as cosine/sine,
• cosecant as 1/sine,
• secant as 1/cosine
• tangent as sine/cosine:

$\tiny{ \tt{ \pink{cos(a)/sin(a) + sin(a)/cos(a) = 1/cos(a) 1/sin(a)}}}$

Put cos(a)/sin(a) + sin(a)/cos(a) over the common denominator

$\large{\mapsto} \small{ \color{navy} \sin(a) \cos(a): \frac{ \cos(a)}{ \sin(a) } + \frac {\sin(a)}{ \cos(a) }= \frac{(cos(a)^2 + sin(a)^2)}{(cos(a) sin(a))}:}$

$\bigstar \tiny{ \color{magenta} \frac{((cos(a)^2 + sin(a)^2)}{(cos(a) sin(a))) }= \frac{1}{(cos(a) sin(a))}}$

• Multiply both sides by

$\bf{ \huge{ \orange \dashrightarrow \sin(a) \cos(a):</p><p> \cos(a)^2 + \sin(a)^2 = 1}}$

• Substitute
• $\color{lime} \bold{ \large{\longmapsto \cos(a)^2 + \sin(a)^2 = 1:</li><li>1 = 1}}$

• The left hand side and right hand side are identical:

$\color{lime}{ \longmapsto \therefore \bold @{The \: Identity \: Is \: Verified™ \: °•° }}$