UPSKILL MATH PLUS
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Learn more1. From the given figure, prove that \(\theta + \phi = 90^{\circ}\). Also prove that there are two other right angled triangles. Find \(sin \ \alpha\), \(cos \ \beta\) and \(tan \ \phi\).
![YCIND20220816_4275_Trignometry_16.png](https://resources.cdn.yaclass.in/79932ea7-1cbf-4dc2-a4bc-94dc27254623/YCIND202208164275Trignometry16w300.png)
Answer:
\(sin \ \alpha =\)
\(cos \ \beta =\)
\(tan \ \phi =\)
2. Verify \(cos \ 90^{\circ} = 1 - 2 \ sin^2 \ 45^{\circ} = 2 \ cos^2 \ 45^{\circ} - 1\)
Proof:
\(cos \ 90^{\circ} =\)
\(1 - 2 \ sin^2 \ 45^{\circ} =\)
\(2 \ cos^2 \ 45^{\circ} - 1 =\)
Thus, \(cos \ 90^{\circ} = 1 - 2 \ sin^2 \ 45^{\circ} = 2 \ cos^2 \ 45^{\circ} - 1\).
Hence, we proved.