Question

If A + B = 90° then the expression tanA secB - cotA cosB is equal to the:
1. tanAsinB
2. tanAsinA
3. cotAcosA
4. cotAcosB

Answer 1

Correct Answer - Option 2 : tanAsinA

Given that:

A + B = 90°

∴ A = 90° - B & B = 90° - A

Calculations:

tanA secB - cotA cosB

secB = sec(90° - A) = cosescA

cosB = cos(90° - A) = sinA

⇒ tanA cosecA - cotA sinA

⇒ (sinA/cosA)cosecA - (cosA/sinA)sinA

∴ sinAcosecA = 1

⇒ 1/cosA - cosA

⇒ (1 - cos²)/cosA

∴ 1 - cos²A =  sin2A

 ⇒ sin2A/cosA

∴ tanA = sinA/cosA

 ⇒ tanA sinA

∴ Given expression is equal to tanAsinA