Question

Cosec square 45 degrees secant square 30 degree sin square 30 degree + 4 cot square 45 degree minus secant square 60 degree

Answer 1

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Answer 2

$\csc^2 45^\circ \sec^2 30^\circ \sin^230^\circ+4\cot^2 45^\circ-\sec^2 60^\circ=\frac{2}{3}$

Step-by-step explanation:

Given : Expression $\csc^2 45^\circ \sec^2 30^\circ \sin^230^\circ+4\cot^2 45^\circ-\sec^2 60^\circ$

To find : The value of the expression ?

Solution :

Expression $\csc^2 45^\circ \sec^2 30^\circ \sin^230^\circ+4\cot^2 45^\circ-\sec^2 60^\circ$

We know the trigonometric values,

$\csc 45^\circ=\sqrt{2}\\\\\sec 30^\circ=\frac{2}{\sqrt{3}}\\\\\sin30^\circ= \frac{1}{2}\\\\\cot 45^\circ=1\\\\\sec 60^\circ=2$

Substitute all,

$=(\sqrt2)^2 (\frac{2}{\sqrt3})^2(\frac{1}{2})^2+4(1)^2-(2)^2$

$=(2)(\frac{4}{3})(\frac{1}{4})+4-4$

$=\frac{2}{3}$

Therefore, $\csc^2 45^\circ \sec^2 30^\circ \sin^230^\circ+4\cot^2 45^\circ-\sec^2 60^\circ=\frac{2}{3}$

#Learn more

Evaluate the following sin 30 degrees + tan 45 degrees minus cos tan 60 degrees by cos 45 degrees + Cos 60 degrees minus secant 30 degrees​

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