Question

show that tan A+ cot A
= sec A, cosec A​

Answer 1

Answer:

LHS:

tan A + cot A

sin A/cos A + cos A/sin A

Take LCM:

(sin²A + cos²A)/ sin A cos A

Remember: sin²A + cos²A = 1

1/sin A. cos A

Remember:  1/sin A = cosec A and

1/cos A = sec A

So,

1/sin A. cos A

sec A. cosec A  = RHS

LHS = RHS

Hence, proved.

Answer 2

Answer:

Hii

Step-by-step explanation:

LHS=

$\tan(a) + \cot(a) = \frac{ \sin(a) }{ \cos(a) } + \frac{ \cos(a) }{ \sin(a) } = \frac{ { \sin }^{2}a + { \cos }^{2}a } {cos \: a \sin \: a } = \frac{1}{ \cos \: a + \sin \: a } = \frac{1}{ \cos(a) } + \frac{1}{ \sin(a) } = \sec(a) + \csc(a)$

=RHS

Hence proved.

Here's your answer.

Hope it helps you.