If 8 tan x =15,then find the value of sin square x - cos square x
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Answer:
the answer is 161/289.............
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Answered by
3
Answer:
Sin²x - Cos²x = 161 / 289
Step-by-step explanation:
8 tan x = 15
tan x = 15/8
tan x = Opposite side / Adjacent side.
Therefore,
(Hypotenuse)² = (Opposite side)² + (Adjacent side)²
(Hypotenuse)² = 15² + 8²
(Hypotenuse)² = 225+64
(Hypotenuse)²=289
Hypotenuse = √289
Hypotenuse = 17.
∴Sin x = Opposite side / Hypotenuse
Sin x = 15 / 17
Sin²x = 225 / 289
Cos x = 8 / 17
Cos²x = 64 / 289
∴Sin²x - Cos²x = 225 / 289 - 64 / 289
Sin²x - Cos²x = (225-64) / 289
Sin²x - Cos²x = 161 / 289
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