Question

Please help me with this question

Answer 1

@mukushla
@amistre64
@AravindG
I want help with question no. 31

Answer 2

@waterineyes
@experimentX
@eliassaab


Sorry to disturb u all.......

actually i m about to complete my exercise...

Answer 3

Which one or all ???

Answer 4

only 31

Answer 5

I got it..

Answer 6

show that\[2 \sec^2 a -\sec^4 a=2(1+\tan^2 a)-(1+\tan^2 a)^2=1-\tan^4 a\]
simplify other part with \(\text{cosec}\) like this to get ur answer

Answer 7

Ok thanks a lot @mukushla
U helped me again......

Answer 8

yw :)

Answer 9

Start by taking common;

\[cosec^2(x)(cosec^2(x) -2) - \sec^2(x)(\sec^2(x) - 2)\]

\[cosec^2(x)(\cot^2(x) - 1) - \sec^2(x)(\tan^2(x) -1)\]

\[-(1 + \cot^2(x))(1 - \cot^2(x)) + (1 + \tan^2(x))(1 - \tan^2(x))\]

\[\implies 1 - \tan^4(x) -1 + \cot^4(x) \implies \cot^4(x) - \tan^4(x)\]

Answer 10

Another nice method.......

Thanks @waterineyes

Answer 11

Using:

\[cosec^2(x) -1 = \cot^2(x)\]

\[\sec^2(x) -1 = \tan^2(x)\]

\[(a +b)(a-b) = a^2 - b^2\]

Answer 12

Welcome..