5) sina cosa sin²a+cos²a+cosa ----------- + --------- = -------------------------=1/sina 1+cosa sina sina(1+cosa)
cosa sina cos²a+sin²a+sina 1+sina 1 -------- + -------- = ------------------------ = ------------------ = -------- 1+sina cosa cosa(1+sina) cosa(1+sina) cosa
Answers & Comments
3b) 5sin⁴a-5cos⁴a=5(sin²a+cos²a)(sin²a-cos²a)=-5cos2a
cos2a=-1 max 5 min -5
4) 1+ctg²a=1+cos²a/sin²a=(sin²a+cos²a)/sin²a=(sin²a+1-sin²a)/sin²a=1/sin²a
sina=0.2 1/sin²a=1/0.2²=25
sin⁴a-cos⁴a=(sin²a+cos²a)(sin²a-cos²a)=sin²a-1+sin²a=2sin²a-1
sina=0.2 2sin²a-1=2*0.2²-1= -0.92
5) sina cosa sin²a+cos²a+cosa
----------- + --------- = -------------------------=1/sina
1+cosa sina sina(1+cosa)
cosa sina cos²a+sin²a+sina 1+sina 1
-------- + -------- = ------------------------ = ------------------ = --------
1+sina cosa cosa(1+sina) cosa(1+sina) cosa
выражение равно 1/sinacosa тождество доказано
6a) sina+cosa=1.3 (sina+cosa)²=sin²a+2sinacosa+cos²a=1+2sinacosa
1.3²=1.69=1+2sinacosa 2sinacosa=0.69 sinacosa=0.345
6b) (sina+cosa)³=sin³a+cos³a+3sin²acosa+3sinacos²a=
= sin³a+cos³a+3sinacosa(sina+cosa) 1.3³=sin³a+cos³a+3*0.345*1.3
sin³a+cos³a=2.197-1.3455=0.8515