Question

using trigonometrical identity. ...correct answer will be marked as brainliest and his or her account will be followed ​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{{sin}^{2} 34 \degree + {sin}^{2} 56 \degree + 2 tan \: 18 \degree \: tan \: 72 \degree - {cot}^{2} 30 \degree = 0}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies {sin}^{2} 34 \degree + {sin}^{2} 56 \degree + 2 tan \: 18 \degree \: tan \: 72 \degree - {cot}^{2} 30 \degree \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies {sin}^{2} 34 \degree + {sin}^{2} 56 \degree + 2 tan \: 18 \degree \: tan \: 72 \degree - {cot}^{2} 30 \degree = ?$

• According to given question :

$\tt: \implies {sin}^{2} 34 \degree + {sin}^{2} 56 \degree + 2 tan \: 18 \degree \: tan \: 72 \degree - {cot}^{2} 30 \degree \\ \\ \tt \circ \: sin \: (90 - \theta) = cos \: \theta \\ \\ \tt: \implies {sin}^{2} 34 \degree + {cos}^{2} 34 \degree + 2 tan \: 18 \degree \: tan \: 72 \degree - {cot}^{2} 30 \degree \\ \\ \tt \circ \: {sin}^{2} \theta + {cos}^{2} \theta = 1 \\ \\ \tt: \implies 1 +2 tan \: 18 \degree \: tan \: 72 \degree - {cot}^{2} 30 \degree \\ \\ \tt \circ \: tan(90 - \theta) = cot \: \theta \\ \\ \tt: \implies 1+ 2 tan \: 18 \degree \: cot \: 18 \degree - {cot}^{2} 30 \degree \\ \\ \tt \circ \:tan \: \theta \times cot \: \theta = 1 \\ \\ \tt: \implies 1+ 2 \times 1 - {cot}^{2} 30 \degree \\ \\ \tt \circ \: cot \: 30 \degree = \sqrt{3} \\ \\ \tt: \implies 1+ 2 - (\sqrt{3})^{2} \\ \\ \tt: \implies 1+ 2 - 3 \\ \\ \tt: \implies 3 - 3 \\ \\ \green{\tt: \implies 0} \\ \\ \green{\tt \therefore {sin}^{2} 34 \degree + {sin}^{2} 56 \degree + 2 tan \: 18 \degree \: tan \: 72 \degree - {cot}^{2} 30 \degree = 0}$

Answer 2

$</p><p>\huge{\tt{\pink{Hello!!! }}}$

$</p><p>\tt{\red{Identities \: Used \: - }}$

$\tt{ \implies{ \purple{ \sin(90 - \theta) = \cos( \theta) }}}$

$</p><p>\tt{\implies{\purple{ { \sin( \theta) }^2 + { \cos( \theta) }^2 = 1 }}}$

$\tt{ \implies{ \purple{ \tan(90 - \theta) = \cot( \theta) }}}$

$\tt{ \implies{ \purple{ \tan( \theta) \times \cot( \theta) = 1 }}}$

$\tt{\implies{\purple{ \tan( 30° ) = \dfrac{1}{ \sqrt{3}} }}}$

Using these identities and solving, we get the Answer as 0.