If 2cosx/(cosx – sinx) – (1 + tanx)/(1 – tanx) = tanα, then, what is the value of (sin2α + cotα)? 

If 2cosx/(cosx – sinx) – (1 + tanx)/(1 – tanx) = tanα, then, what is the value of (sin2α + cotα)?  Correct Answer 2

Given:

2cosx/(cosx – sinx) – (1 + tanx)/(1 – tanx) = tanα

Formula Used:

sin90° = 1, cot45° = 1 and tan45° = 1

Calculation:

2cosx/ (cosx – sinx) – (1 + tanx)/(1 – tanx) = tanα

⇒ 2cosx/ (cosx – sinx) – (1 + sinx/cosx)/(1 – sinx/cosx) = tanα

⇒ 2cosx/ (cosx – sinx) – (cosx + sinx)/(cosx – sinx) = tanα

⇒ (2cosx – cosx – sinx)/(cosx – sinx) = tanα

⇒ (cosx – sinx)/(cosx – sinx) = tanα

⇒ 1 = tanα

⇒ α = 45°

∴ (sin2α + cotα) = sin90° + cot45°

⇒ 1 + 1

⇒ 2