Question

please help me with this question

Answer 1

Solution

Given That :-

• sin θ = 4/5

Find :-

• (sin θ tan θ - 1)/2 tan² θ

Solution

Using trigonometric Formula

★ sin θ = perpendicular/Hypotenuse

★ tan θ = perpendicular/base

We assume that,

∆ ABC is a right triangle .

So, Here

• AB = Perpendicular = 4
• BC = Base
• CA = Hypotenuse = 5

Now, Calculate Hypotenuse,

Using Pythagorean Theorem

★ Hypotenuse² = Base² + Perpendicular²

So,

==> CA = √(AB² + BC²)

Keep all above values,

==> 5 = √(4² + BC²)

==> 5² = 16 + BC²

==> BC² = 25 - 16

==> BC = √9

==> BC = 3

Here, Base = 3

Then,

★ tan θ = perpendicular/base = 4/3

Now, keep all value on (sin θ tan θ - 1)/2 tan² θ

==>( 4/5 × 4/3 - 1)/2 × (4/3)²

==> (16/15 - 1)/(32/9)

==> [(16-15)/15]/(32/9)

==> 1/15 × 9/32

==> 3/(5×32)

==> 3/160

Hence

• Value of (sin θ tan θ - 1)/2 tan² θ will be = 3/160

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Answer 2

Answer:

3/160 is answer of question