Is it true that If cosθ=0.6 then 5sinθ−3tanθ=0 ?

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True

False

answer is A.

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Detailed Solution

Now, from the given question we have cosθ=0.6 ....(a)
Now, by using the trigonometric identity which gives the relation between the function that are mentioned in the hint, we get the following substitute the value from the question and as well as from equation (a)
⇒

θ

θ

=1
Now substitute the cosθ value and find the sinθ value in the above equation then we get
⇒

θ

=1−

{(0.6)}^{2}

⇒

θ

=1−0.36
On simplifying we get as follows
⇒

θ

=0.64
Since the perfect square of 0.64 is 0.8
⇒sinθ=0.8
Therefore, the value of sinθ=0.8s
Now, again from the hint, we know that we can get the tan function as follows
⇒tanθ=

\frac{sinθ}{cosθ}

And now let us substitute the sinθs and cosθ values in tanθ then we get as follows
⇒tanθ=

\frac{0.8}{0.6}

On simplifying we get as follows
⇒tanθ=

\frac{4}{3}

Now, from the given expression in the question, on substituting the values, we have
5sinθ−3tanθ=0
Let us first consider the left hand side and calculate its value L.H.S=5sinθ−3tanθ
And now substitute the sinθ and tanθ values then we get as follows
L.H.S=5×0.8−3×

\frac{4}{3}

On simplifying the above calculation we get as follows
L.H.S=4−4=0
Thus, the value of right hand side is equal to left hand side
Therefore, it is verified that 5sinθ−3tanθ=0
Hence proved.

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