Question

will follow anyone who gives the answer of this 2 questions completely and correctly​

Answer 1

Here is your answer ....

(answer is given on attachment with process )

25) split the 75 into (45 + 30)

then apply the formula

sin (A+B) = sin A cos B + cos A sin B

26) first derive the value of cos and sin from tan , then follow the process as given on attachment .....

Answer 2

Q1) Given that sin(A + B) = sinA.cosB + cosA.sinB, Find sin75°.

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Answer :-

Using trigonometric table, we know that,

sin75 = sin(45 + 30)

• A → 45

• B → 30

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Substituting values of A and B in the question,

sin(45 + 30) = sin45.cos30 + cos45.sin30

→ $sin75 = \frac{1}{\sqrt{2}}.\frac{\sqrt{3}}{2}.\frac{1}{\sqrt{2}}.\frac{1}{2}$

→ $\frac{\sqrt{3}}{2\sqrt{2}}$ + $\frac{1}{2\sqrt{2} }$

→ $\frac{\sqrt{3}+1}{2\sqrt{2}}$

Hence,

Sin75 = $\frac{\sqrt{3}+1}{2\sqrt{2}}$

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Q2) If 3tan$\theta$ = 4, find value of $\frac{4cos\theta-sin\theta}{2cos\theta+sin\theta}$

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Answer :-

In ΔABC,

3tan = 4

Tan = AB/BC = 4/3

Finding the third side by PGT -

AB² + BC² = AC²

4² + 3² = AC²

16 + 9 = AC²

AC = √25

AC = 5

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cos = BC/AC = 3/5

sin = AB/AC = 4/5

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Substituting values in question :-

→ $\frac{4(\frac{3}{5}) -\frac{4}{5} }{2\frac{3}{5} +\frac{4}{5} }$

→ $\frac{\frac{12-4}{5}}{\frac{6+4}{5} }$

→ $\frac{12-4}{6+4}$

→ $\frac{8}{10}$

→ $\frac{4}{5}$

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