Question

Find the value of \(\frac{tan15^\circ\space+\space tan45^\circ}{sin^215^\circ\space-\frac{tan45^\circ}{cot15^\circ}\space +\space cos^215^\circ}\).

Answer 1

Correct Answer - Option 4 : √3

Concept used:

tan(A + B) = (tanA + tanB)/(1 – tanA × tanB)

sin²θ + cos²θ = 1

Calculation:
\(\frac{tan15^\circ\space+\space tan45^\circ}{sin^215^\circ\space-\frac{tan45^\circ}{cot15^\circ}\space +\space cos^215^\circ}\)

⇒ (tan15° + tan45°)/(sin²15° + cos²15° – tan45° × tan15° 

⇒ (tan15° + tan45°)/(1 – tan45° × tan15°) 

⇒ tan(15° + 45°)

⇒ tan60°

⇒ √3

∴ The value of \(\frac{tan15^\circ\space+\space tan45^\circ}{sin^215^\circ\space-\frac{tan45^\circ}{cot15^\circ}\space +\space cos^215^\circ}\) is √3.