1.
B = $cos^{4}x$ - $sin^{4}x$+2 $cos^{2}x$
=($cos^{2}x$ - $sin^{2}x$)($cos^{2}x$ + $sin^{2}x$)+2$cos^{2}x$
=$cos^{2}x$ - $sin^{2}x$+2$cos^{2}x$
=3$cos^{2}x$ - $sin^{2}x$
đề phần này sai rồi bạn ạ
C= 2( $sin^{6}x$ + $cos^{6}x$) -3 ( $sin^{4}x$ + $cos^{4}x$)
=2( $sin^{2}x$ + $cos^{2}x$)( $sin^{4}x$ -$sin^{2}x$. $cos^{2}x$ + $cos^{4}x$) -3 ( $sin^{4}x$ + $cos^{4}x$)
= 2 ( $sin^{4}x$ + $cos^{4}x$) -2 $sin^{2}x$. $cos^{2}x$ -3 ( $sin^{4}x$ + $cos^{4}x$)
=-$sin^{4}x$ -2 $sin^{2}x$. $cos^{2}x$ -$cos^{4}x$
=- ($sin^{2}x$+$cos^{2}x$)$^{2}$ =-1
-> C không phụ thuộc vào x
2.
a. C=cot 1 . cot 2 . cot3....cot44.cot45.cot46....cot87.cot88.cot89
=cot1. cot2. cot3 .....cot44.cot45.tan44.....tan3.tan2.tan1
=(cot1.tan1).(cot2.tan2)....(cot44.tan44).tan45
=1.1.....1. $\frac{\sqrt[]{2}}{2}$= $\frac{\sqrt[]{2}}{2}$
b. D= $cos^{2}1$ + $cos^{2}2$ +$cos^{2}3$ +....+$cos^{2}44$ + $cos^{2}45$ +$cos^{2}46$+.....+$cos^{2}87$ +$cos^{2}88$ +$cos^{2}89$
= $cos^{2}1$ + $cos^{2}2$ +$cos^{2}3$ + ....+$cos^{2}44$+ $cos^{2}45$ + $sin^{2}44$ +....+$sin^{2}3$+ $sin^{2}3$ +$sin^{2}1$
= ($cos^{2}1$+$sin^{2}1$)+($cos^{2}2$+$sin^{2}2$)+....+($cos^{2}44$+$sin^{2}44$)+$cos^{2}45$
=1.44+$\frac{1}{2}$ = $\frac{89}{2}$
