Question

Show that: (1 + cotθ - cosecθ)(1 + tanθ + secθ) = 2.​

Answer 1

Answer:

refer this image

hope it helps ..!(^～^)

Answer 2

Step-by-step explanation:

$\large\bf{\underline{\underline{To\ prove:-}}}$

$\bf : \implies {(1\ cot \theta\ -\ cosec \theta)(1\ +\ tan \theta\ +\ sec \theta)\ =\ 2.}$

$\large\bf{\underline{\underline{Solution:-}}}$

$\bf : \implies {L.H.S\ =\ (1\ cot \theta\ -\ cosec \theta)(1\ +\ tan \theta\ +\ sec \theta)} \\ \\ \\ \bf : \implies {\bigg (1\ +\ \dfrac{cos \theta}{sin \theta}\ -\ \dfrac{1}{sin \theta} \bigg)\ \bigg (1\ +\ \dfrac{sin \theta}{cos \theta}\ +\ \dfrac{1}{cos \theta} \bigg)} \\ \\ \\ \bf : \implies {\bigg (\dfrac{sin \theta\ +\ cos \theta\ -\ 1}{sin \theta} \bigg)\ \bigg (\dfrac{sin \theta\ +\ cos \theta\ +\ 1}{cos \theta} \bigg)} \\ \\ \\ \bf : \implies {\dfrac{(sin \theta\ +\ cos \theta)^2\ -\ 1}{sin \theta\ cos \theta}} \\ \\ \\ \bf : \implies {\dfrac{2\ sin \theta\ cos \theta\ +\ sin^2 \theta\ +\ cos^2 \theta\ -\ 1}{sin \theta\ cos \theta}} \\ \\ \\ \bf : \implies {\dfrac{1\ +\ 2\ sin \theta\ cos \theta\ -\ 1}{sin \theta\ cos \theta}} \\ \\ \\ \bf : \implies {\dfrac{2\ {\cancel {sin \theta\ cos \theta}}}{\cancel {sin \theta\ cos \theta}}} \\ \\ \\ \bf : \implies {\purple{\underline{\boxed{\bf R.H.S\ =\ 2}}}}\bigstar$

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$\begin{gathered}\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar\: Hence\: Proved \bigstar}}}}}\mid}\\\\\end{gathered}$