Question

cosec 30 + cosec 60 + cosec 90 / sec 0 + sec 30 + sec 60​

Answer 1

$\huge\rm\underline\purple{Question :-}$

Evaluate

Cosec 30°+Cosec 60°+Cosec 90°/sec 0°+sec 30°+sec 60°

$\huge\rm\underline\purple{Solution :-}$

$\green{\underline\bold{We\: know,}}$

• Cosec 30° = 2
• Cosec 60° = $\frac{2}{\sqrt3}$
• Cosec 90° = 1
• sec 0° = 1
• sec 30° = $\frac{2}{\sqrt3}$
• sec 60° = 2

$\red{\underline\bold{Putting\: the\:values\:we\:get,}}$

$\frac {Cosec 30°+Cosec 60°+Cosec 90°}{sec 0°+sec 30°+ sec 60°}$

= $\frac {2+\frac{2}{3}\sqrt3+1}{1+\frac{2}{3}\sqrt3+2}$

= $\frac {3+\frac{2}{3}\sqrt3}{3+\frac{2}{3}\sqrt3}$

= 1

$\pink{\underline\bold{ ∴ \:The\:required\:answer\:is\:1.}}$

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Answer 2

Given : cosec 30,cosec 60,cosec 90,sec 0,sec 30,sec 60

To find : cosec 30+ cosec 60+cosec 90/sec 0+ sec 30+ sec 60

SOLUTION:

We know the values:

cosec 30= 2

cosec 30= 2

cosec 60=2/root3

sec0= 1

sec 30=2/root 3

sec 60= 2

Putting all these values in:

= cosec 30+cosec 60+cosec 90/sec 0+sec30 +sec 60

= 2+2/root 3+1/1+2/root 3+2

= 3+2/root3 / 3+ 2/root 3

=1

Answer :Value of cosec 30+cosec 60+cosec 90/sec 0+sec 30+sec 60 is 1