Question

What is the value of
$\sin(theta) {}^{2} + \cos(theta) {}^{2}$
​

Answer 1

Aɴsᴡᴇʀ ᴏғ ᴛʜɪs ǫᴜᴇsᴛɪᴏɴ :

sin²θ + cos²θ = 1

ᴀɴsᴡᴇʀ ᴏғ ʏᴏᴜʀ ᴀɴᴏᴛʜᴇʀ ǫᴜᴇsᴛɪᴏɴ :

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such meetings are very bad and abusive,

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Answer 2

${\huge \bold { \red{\underline{ \color{blue}{A}\color{red}{n} \color{gold}{s} \color{blue}{w} \color{green} {e} \color{red}{r}}}} }$

We know ,

• Sin θ = opposite/hypothesis = O/H
• cos θ = adjacent/hypothesis = A/H

$\leadsto \sf \sin^{2}\theta + \cos ^{2}\theta = {\bigg( \dfrac{ O}{H} \bigg)}^{2} + {\bigg( \dfrac{A}{H} \bigg)}^{2}$

$\leadsto \sf \sin^{2}\theta + \cos^{2} \theta= \dfrac{ {O}^{2} }{{H}^{2} } + \dfrac{ {A}^{2} }{{H}^{2} }$

$\leadsto\sf \sin^{2}\theta + \cos^{2} \theta= \dfrac{ {O}^{2} + {A}^{2} }{{H}^{2} }$

According to Pythagoras theorem.......

O² + A² = H²

$\leadsto \sf \sin^{2}\theta + \cos ^{2}\theta= \cancel \dfrac{{H}^{2}}{{H}^{2} } = 1$

hence, sin²θ + cos²θ = 1

________________

some more formula of trigonometry..

1. sin²θ + cos²θ = 1
2. sec²θ - tan²θ = 1
3. cosec²θ - cot²θ = 1

☄ sin θ = O/H

☄ cosθ = A/H

☄ tan θ = O/A

☄ cot θ = A/O

☄ sec θ = H/A

☄ cosec θ = H/O