Question

tick the correct option and justify your answer : if cos A=4/5,the value of tan A is​

Answer 1

• tan A = 3/4

Step-by-step explanation:

Given:

• cos A = 4/5

To find:

The value of tan A

So,

In cos A = Base/Hypostenuse = B/H = 4/5

Let Base (B) = 4x

And Hypostenuse (H) = 5x

• We can get, the value of Perpendicular (P),

(Perpendicular)² + (Base)² = (Hypotenuse)²

⇒ (P)² = (H)² - (B)²

⇒ (P)² = (5x)² - (4x)²

⇒ (P)² = 25x² = 16x²

⇒ (P)² = 9x²

⇒ P = 3x

[By taking square roots in both the sides]

Now,

tan A = Perpendicula/Baser = P/B

tan A = 3x/4x

∴ tan A = 3/4

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More Information:

• sin A = P/H
• cos A = B/H
• tan A = P/B
• cot A = B/P
• sec A = H/B
• cosec A = H/P

Also,

• sin (90° - A) = cos A
• cos (90° - A) = sin A
• tan (90° - A) = cot A
• cot (90° - A) = tan A
• sec (90° - A) = cosec A
• cosec (90° - A) = sec A

Answer 2

Step-by-step explanation:

cos A = B/H

B= 4

H = 5

SINCE BY PYTHAGORAS THEOREM

(HYP)² = B²+ P²

5² = 4²+ P²

25 = 16 + P²

25-16 = 9

P = 3

Tan A = P/B

= 3/4

HOPE THIS HELPS..