Question

Find the exact value of the expression-

$sec35°csc55°-\tan 35°cot55°$

Short answer

The required value is,

$sec35°csc55°-\tan 35°cot55°=$$1$

Step-by-step solution

Step 1. Given information

Given expression,

$sec35°csc55°-\tan 35°cot55°$

Step 2. Calculation

Solving the given expression,

$$\begin{gathered} sec35°csc55°-\tan 35°cot55° \\ =sec35°csc\left(90°-35°\right)-\tan 35°cot(90°-35°) \\ =sec35°sec35°-\tan 35°\tan 35° \end{gathered}$$ -----------$\left\{csc(90°-\theta )=sec\theta ,cot(90°-\theta )=\tan \theta \right\}$

$$\begin{gathered} =se{c}^{2}35°-{\tan }^{2}35° \\ =1 \end{gathered}$$ -------------we know,$1+{\tan }^2\theta =se{c}^2\theta$