Find out the value of sec15∘
Step 1: Convert it into cosine form
Firstly, we will find the value of cos15°.
cos15°=cos(45°-30°)By using the formula,
cos(a-b)=cosacosb+sinasinb
Here,
a=45°and b=30°
cos15°=cos45°cos30°+sin45°sin30°
Step 2: Finding the value in cosine form and then converting it into secant.
⇒cos15∘=12×32+12×12⇒cos15∘=322+122⇒cos15∘=3+122
Therefore,
⇒sec15∘=1cos15∘⇒sec15∘=13+122⇒sec15∘=223+1
Hence,sec15∘=223+1
If sec θ + tan θ = x, find the value of sec θ.