Question

SecΦ+tanΦ=k then value of sinΦ

Answer 1

sec + tan = k
=> 1/cos + sin / cos = k
=> 1+sin = k•cos
=> sin= k•cos - 1

Answer 2

$\textbf{sec} \theta \: + \textbf{tan} \theta \: = \textbf{k} \\ \\ \rightarrow \: \frac{1}{ \text{cos} \theta} \: + \frac{ \text{sin} \theta}{ \text{cos} \theta} = \text{k} \\ \\ \rightarrow \: \frac{1 \: + \text{sin} \theta}{ \text{cos} \theta} \: = \text{k} \\ \\ \rightarrow \: 1 \: + \text{sin} \theta \: = \text{k.cos} \theta \\ \\ \rightarrow \: \text{sin} \theta \: = \: \text{k.cos} \theta - 1 \\ \\ \boxed{\textsf{sin} \theta \: = \: \textsf{k.cos} \theta - 1}$