Question

In Fig 5.47, the value of $cos\Phi$ is
(a)$\frac{5}{4}$
(b)$\frac{5}{3}$
(c)$\frac{3}{}$
(d)$\frac{4}{5}$

Answer 1

Given : From figure 5.47, AB (P) = 4 , BC (B) = 3 , AC (H) = 5

To find : the value of cos ϕ is

Solution :  

 We know that the sum of the angles of the straight line is 180°.

∴ ∠ θ + ∠90° + ∠ϕ = 180°

∠ θ  + ∠ϕ = 180° - 90°

∠ θ + ∠ϕ = 90°

∠ θ  = 90° - ∠ϕ ……….(1)

 

In ∆ABC,

sin θ = P/H = 4/5  

From eq 1 we obtain ,  

sin (90 - ϕ) = 4/5

We know that sin (90° -  θ ) = cos θ  

Sin (90 - ϕ) = cos ϕ  

∴ cos ϕ = 4/5

Hence the value of cos ϕ is ⅘ .

Among the given options option (D) ⅘ is  correct.

Hope this answer will help you…

 

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The value of$\frac{tan55^{0}}{cot35^{0} }+cot 1^{0}cot2^{0}+cot3^{0}....cot90^{0}$, is

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Answer 2

☺☺Hope it's help you☺☺

We know that the sum of all the angles on one side of a straight line is 180° . These angles are said to be in linear pair.

Therefore, using the figure, we get