Question

if secθ+tanθ=4,than secθ-tanθ=?

Answer 1

$\underline{\underline{\mathfrak{\Large{Solution : }}}} \\ \\ \\ \underline {\sf {Given,}} \\ \\ \\ \sf\: Sec\theta + tan\theta = 4 \\ \\ \\ \underline {\sf {To\: Find :}} \\ \\ \\ \sf\: Sec\theta - Tan\theta \\ \\ \\ \underline {\sf {Procedure :}} \\ \\ \\ \underline {\sf {By\: using\: Trigonometry \: Identity :}} \\ \\ \\ \large {\boxed {\sf { Sec^2 \theta - Tan^2 \theta = 1 }}} \\ \\ \\ \sf\implies\: (Sec\theta - Tan\theta)(Sec\theta + Tan\theta) = 1 \\ \\ \\ \sf\implies\:(4)(Sec\theta - Tan\theta) = 1 \\ \\ \\ \large {\boxed {\sf { Sec\theta - Tan\theta = \dfrac {1}{4}}}}$

Answer 2

Solution:-

Given:-

secθ + tanθ = 4

To Find:-

secθ - tanθ = ?

Find:-

We know that,

( sec²θ - tan²θ ) = 1

=) ( secθ - tanθ ) ( secθ + tanθ ) = 1

Substituting [ secθ + tanθ = 4 ]. we get,

=) ( secθ - tanθ ) (4) = 1

=) secθ - tanθ = 1/4

Hence,

secθ - tanθ = 1/4

Trigonometric Formulas:-

• cos²θ + sin²θ = 1
• sec²θ - tan²θ = 1
• cosec²θ - cot²θ = 1