Math, asked by ayrytsiyfouguovkhvih, 4 months ago

if 10 theta = 1/ root 7
show that cosec ² theta - sec ²theta
upon cosec²theta + sec²theta =3/4​

Answers

Answered by Anonymous
16

Question :

If tan θ = ¹/√7 then , show that  \sf \dfrac{csc^2\theta-sec^2\theta}{csc^2\theta+sec^2\theta}=\dfrac{3}{4}

Solution :

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\sf tan\ \theta=\dfrac{1}{\sqrt{7}}

:\to \sf tan^2\theta=\dfrac{1}{(\sqrt{7})^2}

:\to \sf \textsf{\textbf{\pink{tan$^\text{2} \boldsymbol \theta\ $ =\ $\dfrac{\text{1}}{\text{7}}$}}}\ \; \bigstar

\sf \dfrac{1}{cot\ \theta}=\dfrac{1}{\sqrt{7}}

:\to \sf cot\ \theta=\sqrt{7}

:\to \sf cot^2\theta=(\sqrt{7})^2

:\to \sf \textsf{\textbf{\green{cot$^\text{2}\ \boldsymbol \theta $\ =\ 7}}}\ \; \bigstar

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LHS

:\to \bf \blue{\dfrac{csc^2\theta-sec^2\theta}{csc^2\theta+sec^2\theta}}

From Trigonometric identities ,

csc²θ = 1 + cot²θ

sec²θ = 1 + tan²θ

:\to \sf \dfrac{(1+cot^2\theta)-(1+tan^2\theta)}{(1+cot^2\theta)+(1+tan^2\theta)}

tan²θ = ¹/₇

cot²θ = 7

:\to \sf \dfrac{(1+7)-(1+\frac{1}{7})}{(1+7)+(1+\frac{1}{7})}

:\to\ \sf \dfrac{8-\frac{8}{7}}{8+\frac{8}{7}}

:\to\ \sf \dfrac{48}{64}

:\to\ \textsf{\textbf{\orange{$\dfrac{\text{3}}{\text{4}}$}}}\ \; \bigstar

RHS

Answered by 240guriya
0

Answer:

This is the answer........

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