Question

without using trigonometric table, evaluate
sec11/cosec79​

Answer 1

AmswEr:-

The Required Answer Is 1.

ExplanaTion:-

To Evaluate:-

• $\tt\dfrac{sec\ 11\degree}{cosec\ 79\degree}.$

ID Used:-

$\tt\leadsto sec \theta = cosec(90 - \theta).$

By Using Above ID:-

$\tt\mapsto \dfrac{ \sec \: 11 \degree}{cosec \:79 \degree} .$

$\tt = \dfrac{cosec(90 - 11) \degree}{cosec\:79 \degree} \: \: \rm(by \: using \: id).$

$\tt = \cancel \dfrac{cosec \: 79 \degree}{cosec \: 79 \degree} .$

$\large\boxed{ \bf = 1.}$

Therefore $\bf\dfrac{sec\ 11\degree}{cosec\ 79\degree} = 1$

More related trigonometric IDs:-

$\tt\longrightarrow \cos\theta = \sin(90-\theta).$

$\tt\longrightarrow \sin\theta = \cos(90-\theta).$

$\tt\longrightarrow \tan\theta = \cot(90-\theta).$

$\tt\longrightarrow \cot\theta = \tan(90-\theta).$

$\tt\longrightarrow cosec\theta = \sec(90-\theta).$

Answer 2

${ \bf{ \underline{Question}}}$

Without using trigonometric table, evaluate

${ \mathtt{ \dfrac{sec11}{cosec79}}}$

${ \bf{ \underline{Answer}}}$

${ \text{By \: using \: identity }}$

${ \text{sec }\theta} = { \text {cosec (90 - } \theta})$

$\implies{ \mathtt{ \dfrac{sec11}{cosec79}}}$

$\implies { \mathtt{ \dfrac{sec(90 - 79)}{cosec79}}}$

$( \therefore{ \text{sec(90 - }} \theta).{ \text{cosec}} \theta)$

$\implies{ \mathtt{ \dfrac{cosec79}{cosec79}}}$

$\implies{ \text{1}}$

SOME OTHER TRIGNOMETRIC IDENTITIES :-

• csc(θ) = csc(θ) = 1/sin(θ)

• sec(θ) = sec(θ) = 1/cos(θ)

• cot(θ) = cot(θ) = 1/tan(θ)

• tan(θ) = tan(θ) = sin(θ)/cos(θ)

• cot(θ) = cot(θ) = cos(θ)/sin(θ)

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