Question

Example 7. Prove that:

√1-sin² (90°-theta)

+√4-4 sin² (90° – theta) = 3 sin theta

Kindly help me ​

Answer 1

Answer:

Given,

$L.H.S = \sf \sqrt{1 - {sin}^{2} (90 - \theta)} \: + \: \sqrt{4 - 4 \: {sin}^{2} (90 - \theta)} \\ \sf \: = \sqrt{1 - {cos}^{2} \theta} + \sqrt{4 - 4 \: {cos}^{2} \theta} \\ \sf \: = \sqrt{ {sin}^{2} \theta } + \sqrt{4(1 - {cos}^{2} \theta)} \\ \sf \: = sin \: \theta + \sqrt{4 \: {sin}^{2} \theta } \\ \sf \: = sin \: \theta + \sqrt{ {(4sin \: \theta)}^{2} } \\ \sf \: = sin \: \theta + 2sin \: \theta \\ \sf \: = 3sin \: \theta \: \\ = R.H.S \\ \\ \huge \underline{\green{ \bf \: hence \: proved}}$

Note:

$>\: {sin}^{2} \:(90 - \theta) \\ = \{{sin(90 - \theta)} \}^{2} \\ = {(cos \: \theta)}^{2} \\ = {cos}^{2} \: \theta \:$

$> \: sin(90 - x) = cos \: x \\ \\ > cos(90 - x) = sin \: x \\ \\ > \: {sin}^{2} \: x + {cos}^{2} \: x = 1 \\ \therefore \: {sin}^{2} \: x = 1 - {cos}^{2} \: x \\ \\ \:$

Answer 2

Answer:

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Step-by-step explanation:

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