Is $(\sin \phi)^2$ is equal to $\sin^2\phi$?
Can any one tell what is the ans for the below expression
$\sin^260$ + $\cos^260$ + $\tan^245$ + $\sec^260$ - $\csc^260$
Is $(\sin \phi)^2$ is equal to $\sin^2\phi$?
Can any one tell what is the ans for the below expression
$\sin^260$ + $\cos^260$ + $\tan^245$ + $\sec^260$ - $\csc^260$
($sin \phi$)^2 is equal to $sin^2\phi$.
$sin^260$ + $cos^260$ + $tan^245$ + $sec^260$ - $cosec^260$
The trick to that is to use a few trigonometric identities.
$\sin^2\theta + \cos^2\theta = 1$
$\tan 45 = 1$
The value of $\cos 60$ is $\frac{1}{2}$, so $\sec^260$ will evaluate to 4. The value of $\sin 60$ is $\sqrt{\frac{3}{4}}$, so $\csc^260$ will evaluate to $\frac{4}{3}$.
Adding it all up you have $1 + 1 + 4 - \frac{4}{3} = \frac{14}{3}$
Yes, $sin^2\phi$ is by definition $(sin\phi)^2$. The answer to the last question is: you can calculate sin(60), cos(60) and tan(45) just using Pythagoras. A hint for the first two of these: draw a right angled triangle with one angle of 60 degrees. What is the third angle? Can you exploit the symmetry?