Question

Assertion (A): 5 tan θ = 4 then sin θ = 4, cos θ = 5

Reason (R): tan θ = `sin θ/cos θ`

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

A is false but R is true.

Explanation:

5 tan θ = 4 ⟹ tan θ = `4/5`

opposite side = 4, adjacent side = 5 = hypotenuse = `sqrt41`

sin θ = `4/sqrt41, cos θ = 5/sqrt41` not 4 & 5 Assertion is false.

= tan θ = `sin θ/cos θ` is a correct identity, and the reason is true.