Question

What is the value of cosec² 30° + sin² 45° + sec² 60° +tan² 30°?

Answer 1

Answer:

53/6

Step-by-step explanation:

cosec² 30° + sin² 45° + sec² 60° +tan² 30°

//Cosec30 = 1/Sin30 = 2, sin45 = 1/√2, Sec60 = 1/cos60 = 2, tan30 =1/√3

= (2)² + (1/√2)² + (2)² + (1/√3)²

= 4+ 1/2+4+1/3

= 8 + 5/6 = 53/6

Answer 2

$\csc^2(30)+\sin^2(45)+\sec^2(60)+\tan^2(30)=8.83$

Step-by-step explanation:

Given : Expression $\csc^2(30)+\sin^2(45)+\sec^2(60)+\tan^2(30)$

To find : What is the value of expression ?

Solution :

Expression $\csc^2(30)+\sin^2(45)+\sec^2(60)+\tan^2(30)$

Using trigonometric values,

$\csc(30)=2$, $\sin (45)=\frac{1}{\sqrt{2}}$ , $\sec(60)=2$, $\tan(30)=\frac{1}{\sqrt3}$

Substitute the values,

$=(2)^2+(\frac{1}{\sqrt2})^2+(2)^2+(\frac{1}{\sqrt3})^2$

$=4+\frac{1}{2}+4+\frac{1}{3}$

$=\frac{1}{2}+\frac{1}{3}+8$

$=\frac{3+2+48}{6}$

$=\frac{53}{6}$

$=8.83$

Therefore, $\csc^2(30)+\sin^2(45)+\sec^2(60)+\tan^2(30)=8.83$

#Learn more

Sin²45°. cosec² 30– sec² 60°

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