Question

If sin theta=4/5 find the value of sin theta tan theta -1 /2tansquare theta

Answer 1

As We know that the value of sin ∅ = ⅘ as Well.

→ sin ∅ = P/H

→ sin ∅ = ⅘

Now, By using the Pythagoras theorem, we can find the Base of the triangle.

→ H² = B² + P²

→ 5² = B² + 4²

→ 25 = B² + 16

→ 25 - 16 = B²

→ 9 = B²

→ B = 3

Finally, we're going to get the value of sin∅ tan∅ – ½tan²∅

→ ⅘ × 4/3 - ½ × (4/3)²

→ 16/15 - ½ × (16/9)

→ 16/15 – 8/9

→ (48 –40)/45

→ 8/45

Hence,

The value of sin∅ tan∅ – ½tan²∅ is 8/45.