Question

If θ = 45⁰, then sec θ cot θ - cosec θ tan θ is ________

Answer 1

$$\begin{gathered} \mathrm{sec\theta }\mathrm{cot\theta }-\mathrm{cosec\theta }\mathrm{tan\theta }=\sec {45}^0\cot {45}^0-\mathrm{cosec}{45}^0\tan {45}^0\left[\mathrm{Put}\mathrm{\theta }={45}^0\right] \\ =\sqrt{2}\times 1-\sqrt{2}\times 1 \\ =\sqrt{2}-\sqrt{2} \\ =0 \\ \mathrm{Hence},\mathbf{sec\theta }\mathbf{}\mathbf{cot\theta }\mathbf{-}\mathbf{cosec\theta }\mathbf{}\mathbf{tan\theta }\mathbf{=}\mathbf{0} \end{gathered}$$