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If Sin θ = `A/B`,Show that `(Sectheta + Tan Theta) = Sqrt((B+A)/(B-a))` - Mathematics

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If sin θ = `a/b`,show that `(sectheta + tan theta) = sqrt((b+a)/(b-a))`

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Solution

LHS = (sec θ + tan θ)

= `1/costheta + sintheta/costheta`

=`(1+sintheta)/costheta`

=`(1+sintheta)/sqrt(1-sin^2theta)`

=`((1+a/b))/sqrt(1-(a/b)^2)`

=`((1/1+a/b))/sqrt(1/1-a^2/b^2)`

=`(((b+a)/b))/sqrt((b^2-a^2)/b^2)`

=`((b+a))/(sqrt(b+a)sqrt(b-a)`

=`sqrt((b+a))/(sqrt((b-a)))`

=`sqrt((b+a)/(b-a))`

= RHS

Concept: Trigonometric Ratios and Its Reciprocal
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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 5 Trigonometric Ratios
Q 16
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