Use trigonometric identities to transform the left side of the equation into the right side $$(0<\theta <\pi /2)$$

$$\mathrm{sin}\theta \mathrm{csc}\theta =1$$

$$\mathrm{sin}\theta \mathrm{csc}\theta =1$$

Alexander Lewis
2022-10-24
Answered

Use trigonometric identities to transform the left side of the equation into the right side $$(0<\theta <\pi /2)$$

$$\mathrm{sin}\theta \mathrm{csc}\theta =1$$

$$\mathrm{sin}\theta \mathrm{csc}\theta =1$$

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latatuy

Answered 2022-10-25
Author has **12** answers

We have given

$$0<\theta <\frac{\pi}{2}\phantom{\rule{0ex}{0ex}}\mathrm{sin}\theta \mathrm{csc}\theta =1$$

Taking left side equation

$$LHS=\mathrm{sin}\theta \mathrm{csc}\theta \phantom{\rule{0ex}{0ex}}=(\mathrm{sin}\theta )(\frac{1}{\mathrm{sin}\theta})\phantom{\rule{0ex}{0ex}}=1=RHS$$

Hence $$\mathrm{sin}\theta \mathrm{csc}\theta =1$$

$$0<\theta <\frac{\pi}{2}\phantom{\rule{0ex}{0ex}}\mathrm{sin}\theta \mathrm{csc}\theta =1$$

Taking left side equation

$$LHS=\mathrm{sin}\theta \mathrm{csc}\theta \phantom{\rule{0ex}{0ex}}=(\mathrm{sin}\theta )(\frac{1}{\mathrm{sin}\theta})\phantom{\rule{0ex}{0ex}}=1=RHS$$

Hence $$\mathrm{sin}\theta \mathrm{csc}\theta =1$$

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