If tan theta =✓3×sin theta then what is the value of 2cos square theta
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✓3 tanθ = 3 sinθ
✓3 sinθ/cosθ = 3 sinθ
✓3 will cut 3 and sin theta wil be cancelled
1/cosθ = ✓3
cosθ = 1/✓3
Squaring on both sides :
cos²θ = 1/3. ...... equation (1)
1-sin²θ = 1/3
sin²θ = 1 - 1/3
sin²θ = 2/3. ....... equation (2)
Now,
Subtracting equation (1) from (2)...
sin²θ - cos²θ = (2/3)² - (1/3)²
= 4/9 - 1/9
= 3/9
= 1/3 - Answer
✓3 sinθ/cosθ = 3 sinθ
✓3 will cut 3 and sin theta wil be cancelled
1/cosθ = ✓3
cosθ = 1/✓3
Squaring on both sides :
cos²θ = 1/3. ...... equation (1)
1-sin²θ = 1/3
sin²θ = 1 - 1/3
sin²θ = 2/3. ....... equation (2)
Now,
Subtracting equation (1) from (2)...
sin²θ - cos²θ = (2/3)² - (1/3)²
= 4/9 - 1/9
= 3/9
= 1/3 - Answer
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