Question

If Tan theta = cot theta , then find the value of 3 sin theta -2 cos theta+ sec theta​

Answer 1

Answer:

Let theta = x

$tanx = cotx \\ tanx = \frac{1}{tanx} \\ {tan}^{2} x = 1 \\ tanx = 1 \\ x = 45 \\ consider \: 3sinx - 2cosx + secx \\ = 3sin45 - 2cos45 + sec45 \\ = 3 \times \frac{1}{ \sqrt{2} } - 2 \times \frac{1}{ \sqrt{2} } + \sqrt{2} \\ = \frac{3 - 2 + 2}{ \sqrt{2} } \\ = \frac{3}{ \sqrt{2} } \\ = \frac{3}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } \\ = \frac{3 \sqrt{2} }{2}$