Question

prove that. | class 10 TRIGONOMETRY. ​

Answer 1

$\bf\large\blue{Question\::-}$

$Prove \: that \: { \sec }^{4} \theta - { \sec }^{2} \theta = {tan}^{4} \theta + {tan}^{2} \theta$

$\bf\large\blue{Answer\::-}$

Formula to be used :

$1 + \tan {}^{2} \theta = sec {}^{2} \theta$

Solution :-

L.H.S

${sec}^{4} \theta - sec {}^{2} \theta$

$= (1 + tan {}^{2} \theta) {}^{2} - 1 + tan {}^{2} \theta$

$= \cancel 1 + tan {}^{4} \theta + 2 \: tan \: \theta \: \cancel{- 1 }- tan \: \theta$

$= \tan ^{4} \theta + tan \: \theta = R.H.S$

Therefore, L.H.S = R.H.S .

HENCE PROVED !

_________________________________________

HOPE IT HELPS YOU : )

Answer 2

Answer:

hope it helps you

Step-by-step explanation:

pls mark as brainlist