Answer this 9th question

Answer this 9th question (c) Sec 9. In the adjoining figure, ABC is an isosceles triangle in which AB AC. Find the values of the following: (a) tan e (b) sin (900 - e) (c) sec 9 + (900 — 0) 'J finding values of trigonometric ratios and expressions from given trigonometric ratio(s) 1

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In △ ADC, by pythagoras theorem AD = \sqrt{{AC}^{2} - {CD}^{2}} = \sqrt{5^{2} - 3^{2}} = \sqrt{25 - 9} = \sqrt{16} = 4 cm Since AB = AC, So, AB = 5 cm Similarly in △ ABD, by pythagoras theorem BD = \sqrt{{AB}^{2} - {AD}^{2}} = \sqrt{5^{2} - 4^{2}} = \sqrt{25 - 16} = \sqrt{9} = 3 cm a) tanθ = \frac{BD}{AD} = \frac{3}{4} b) \sin (90 ° - θ) = cosθ = \frac{AD}{AB} = \frac{4}{5} c) secθ + \cos (90 ° - θ) = secθ + sinθ = \frac{AB}{AD} + \frac{BD}{AB} = \frac{5}{4} + \frac{3}{5} = \frac{37}{20}

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