Question

If $cosA=\frac{7}{25}$, find the value of tan A + cot A.

Answer 1

Answer:

The value of tanA + cot A is  625/168.

Step-by-step explanation:

Given :

cos A = 7/25 …….(1)

By using an identity , sin² θ + cos² θ = 1

sin²A + (7/25)²  = 1

sin²A + 49/625 = 1

sin²A = 1 - 49/625

sin²A = (625 - 49)/625

sin²A = 576/625

sinA = √576/625

sinA = 24/25  …….(2)

tanA + cot A  (Given)

sin A /cosA + cosA/sinA

[By using the identity, cotθ = cosθ/sinθ  ,  tanθ = sinθ/cosθ ]

= (24/25)/(7/25) + 7/25/(24/25)

[From eq 1 & 2]

= 24/25 × 25/7 + 7/25 × 25/24

= 24/7 + 7/24

= (24 × 24 + 7 × 7)/168

= (576 + 49)/168

= 625/168

tanA + cot A = 625/168

Hence, the value of tan A + cot A is  625/168.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

According to the Question:

Refer to the attachment for step-by-step-explanation with answer.

⇒ tan A + cot A = 625/168 ___[ANSWER]