Question

sin A=2/5,find the value of 5+4cotsquare A

Answer 1

Answer:

Step-by-step explanation:

answer is 26 because

sin = opposite / hypotenuse

cot = adjacent / opposite

sin A = 2 / 5

so by pythagoras theorem, 2^2 + x^2 = 5^2

                                           4 + x^2 = 25

                                             x^2 = 21

                                                 x= sqrt 21 = adjacent value

cot^A = 21 / 4

therefore 5 + 4 cot^A = 5 + 4(21/4)

                                  = 5 + 21

                                  = 26

Answer 2

$\textbf{ solution–}$

$sinA = \frac{2}{5} \\ \\ \frac{P }{H } = \frac{2}{5} \\ \\ P = 2 \: \: \: \: \: \: \: \: \: \: \: \: H = 5$

Now,

By Pythagoras theorem

H² = P² + B²
5² = 2² + B²
B² = 5² – 2²
B² = 25 – 4
B² = 21
B = √21

The value of( 5 + 4 cot²A ).

$5 + 4cot ^{2} A \\ \\ = 5 + 4( \frac{B}{P} ) ^{2} \\ \\ = 5 + 4( \frac{\sqrt{21}}{ 2} ) ^{2} \\ \\ = 5 + 4 \times \frac{21}{4} \\ \\ = 5 + 21 = 26$

So, The value of( 5 + 4 cot²A ) is 26

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$\textbf{ Thanks}$