Please help me with this question

Question

vishweshshrimali5 · Answer

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

vishweshshrimali5 · Answer

@waterineyes 
@experimentX 
@eliassaab 


Sorry to disturb u all.......

actually i m about to complete my exercise...

anonymous · Answer

Which one or all ???

vishweshshrimali5 · Answer

only 31

anonymous · Answer

I got it..

anonymous · Answer

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

vishweshshrimali5 · Answer

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

anonymous · Answer

yw :)

anonymous · Answer

Start by taking common;

$$cosec^2(x)(cosec^2(x) -2) - \sec^2(x)(\sec^2(x) - 2)$$

$$cosec^2(x)(\cot^2(x) - 1)  - \sec^2(x)(\tan^2(x) -1)$$

$$-(1 + \cot^2(x))(1 - \cot^2(x)) + (1 + \tan^2(x))(1 - \tan^2(x))$$

$$\implies 1 - \tan^4(x) -1 + \cot^4(x) \implies \cot^4(x) - \tan^4(x)$$

vishweshshrimali5 · Answer

Another nice method.......

Thanks @waterineyes

anonymous · Answer

Using:

$$cosec^2(x) -1 = \cot^2(x)$$

$$\sec^2(x) -1 = \tan^2(x)$$

$$(a +b)(a-b) = a^2 - b^2$$

anonymous · Answer

Welcome..