Question

cosec2theta - cot2theta =1​

Answer 1

Answer:

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Answer 2

Question:

• Prove that : $\sf cosec^2\theta-\cot^2\theta=1$

Solution:

We know that,

$\red\bigstar\;\;\boxed{\sin^2\theta+\cos^2\theta=1}$

$\longmapsto \sin^2\theta+\cos^2\theta=1 \\\\\\\star\; \bf Divide \;both\;sides\;by\; \sin^2\theta \\\\\implies\sf \dfrac{ \sin^2\theta}{ \sin^2\theta}+\dfrac{\cos^2\theta}{\sin^2\theta}=\dfrac{1}{\sin^2\theta}\\\\\\\implies \sf 1+\cot^2\theta= cosec^2\theta\\\\\star\;\bf Moving\;\cot^2\theta \;from\;left\;side\;to\;right\;side\\\\\implies \sf1=cosec^2\theta-\cot^2\theta\\\\\implies \sf cosec^2\theta-\cot^2\theta=1$

$\\\displaystyle\tt\large\quad\underline{\red{Hence\;proved}}\;...!\,$

$\green{\underbrace{\red{\sf Trigonometric\;properties}}}:$

• Cotθ = Cosθ/Sinθ

• Cosecθ = 1/Sinθ

• tanθ = Sinθ/Cosθ
• Secθ = 1/Cosθ
• tanθ = 1/cotθ