Question

if sin theta=4/5,find the value of sin theta tan theta-1/2tan²theta

Answer 1

Answer:

8/45....................

Answer 2

Solution:

Given,

Sin Ф = 4/5

We know that, Sine value of an angle is given as:

$\boxed{ Sin\theta = \dfrac{Opposite}{Hypotenuse}}$

Comparing the given information we get:

• Opposite = 4 units
• Hypotenuse = 5 units

Adjacent side value can be found out by using Pythagoras theorem.

According to Pythagoras theorem,

→ Opposite² + Adjacent² = Hypotenuse²

→ 4² + x² = 5²

→ 16 + x = 25

→ x² = 25 - 16

→ x² = 9

→ x = 3 units

Hence Adjacent Side is 3 units.

We know that,

$\boxed{ Tan\theta = \dfrac{Opposite}{Adjacent}}$

Hence substituting the values we get:

→ Tan Ф = 4/3

According to the question, we have to find the value of:

→ SinФ × TanФ - 1/2 Tan²Ф

Substituting the values we get:

$\implies \dfrac{4}{5} \times \dfrac{4}{3} - \dfrac{1}{2} \times \dfrac{4^2}{3^2}\\\\\implies \dfrac{16}{15} - \dfrac{16}{18}\\\\\\\text{Taking LCM we get:}\\\\\implies \dfrac{16 \times 6 - 16 \times 5}{90}\\\\\implies \boxed{\dfrac{16}{90} = \dfrac{8}{45}}$