If θ be acute angle and cosθ = 15/17, then the value of cot (90° - θ) is??
Answers
Given :
If θ be acute angle and cos θ = 15/17.
To find :
The value of cot (90° - θ) is what ?
Solution :
Cosθ = 15/17
METHOD : 1
According to the trigonometry identities
cos²θ + sin²θ = 1
→ sin²θ = 1 - cos²θ
→ sinθ = √1 - cos²θ
Put the value of cosθ
→ sinθ = √1 - (15/17)²
→ sinθ = √1 - 225/289
→ sinθ = √289 - 225/289
→ sinθ = √64/289
→ sinθ = 8/17
Now the value of cot (90° - θ)
→ cot (90° - θ)
→ tanθ
→ sinθ/cosθ
Substitute the values
→ 8/17/15/17
→ 8/17 × 17/15
→ 8/15
━━━━━━━━━━━━━━━━━━━━━━━━
METHOD : 2
Solve this question by the Pythagoras theorem
★(hypotenuse)²=(base)²+ (perpendicular)²
As we know that
→ cos θ = base/hypotenuse
→ cosθ = 15/17
Let the perpendicular be x , base be 15x and hypotenuse be 17x
According to the theorem
→ (17x)² = (15x)² + (x)²
→ 289x² = 225x² + x²
→ x² = 289x² - 225x²
→ x² = 64x²
→ x = √64x² = 8x
Now the value of cot (90° - θ)
→ cot (90° - θ)
→ tanθ
→ perpendicular/base
→ 8x/15x
→ 8/15
•°• The value of cot (90° - θ) is 8/15
━━━━━━━━━━━━━━━━━━━━━━━━
Answer:
8/15
Step-by-step explanation:
I hope it is helpful