Find the value of \frac{{sin{\ }}^2A+{sin{\ }}^2D}{sin{A\sec{D}}}

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Solution

Q.
Riya and her sister visited their friend’s farmhouse. Upon arrival, Riya noticed that the roof of her friend’s house was shaped like a trapezium, with the dimensions indicated in the figure.

On the basis of above information, answer the following questions:

(iii) (b) $F i n d t h e v a l u e o f \frac{{s i n}^{2} A + {s i n}^{2} D}{s i n A \sec D}$

1 1

2 2

3 5

4 4

Ans.
(1)

We have,

$\frac{{s i n}^{2} A + {s i n}^{2} D}{s i n A \sec D} = \frac{{s i n}^{2} 30 ° + {s i n}^{2} 60 °}{s i n 30 ° s e c 60 °} [∵ ∠ A = 30 ° \Rightarrow ∠ D = 60 °] = \frac{{(\frac{1}{2})}^{2} + {(\frac{\sqrt{3}}{2})}^{2}}{\frac{1}{2} \times 2} = \frac{\frac{1}{4} + \frac{3}{4}}{1} = \frac{1}{1} = 1$

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