Consider the following statements 1 2 If 3 tan cot 5 cosec whereo 0 lt lt 90o th...........

Quantitative Aptitude (CDS) Trignometry

Consider the following statements :

1. $if\: \; \frac{cos\Theta }{1-sin\Theta }+\frac{cos\Theta }{1+sin\Theta }=4 where\, 0<\Theta <90^{o}\, then \Theta =60^{o}$

2. If 3 tan $\Theta$ + cot $\Theta$ = 5 cosec $\Theta$ , whereo 0 < $\Theta$ <90^o , then $\Theta$ = 60^o.

Which of the statements given above is/are correct?

1 only

2 only

Both 1 and 2

Neither 1 nor 2

$if\: \; \frac{cos\Theta }{1-sin\Theta }+\frac{cos\Theta }{1+sin\Theta }=4 where\, 0<\Theta <90^{o}\, then \Theta =60^{o}$

put $\Theta$ =60

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

=4 Hence, (1) is true.

If 3 tan $\Theta$ + cot $\Theta$ = 5 cosec $\Theta$

put $\Theta$ =60^o L.H.S

3 tan60^o+cot 60^o

$3*\sqrt{3}+\frac{1}{\sqrt{3}}=\frac{9+1}{\sqrt{3}}=\frac{10}{\sqrt{3}}$

put $\Theta$ =60^o R.H.S

5 cosec 60^o

$5*\frac{2}{\sqrt{3}}=\frac{10}{\sqrt{3}}$

Hence (2) is also true.

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