Վարժ. 131

ա) sin27°cos3°+cos27°sin3°=sin30°=1/2=0,5

բ) cos87°cos27°+sin87°sin27°=cos60°=1/2=0,5

Վարժ. 132

ա)(sin π/15 +cos π/10)² + (cos π/15 +sin π/10)²=3

sinπ/15² + 2sinπ/15cos×π/10 + cosπ/10²+cosπ/15²+2cosπ/15×sinπ/10 + sin π/10²=2+( 1/2 -sinπ/30)+( 1/2 +sinπ/30)=2+ 1/2 -sinπ/30+1/2+sinπ/30=3

բ) (cos π/9 -cos 2π/9)² + (sin π/9 +sin 2π/9)²=1

cos π/9² – 2cos π/9×cos 2π/9 + cos 2π/9² + sin π/9 + 2sin π/9×sin 2π/9 + sin 2π/9²=2-(cos π/9 + 1/2)+cos π/9 -1/2=2-cos π/9 – 1/2 + cos π/9 – 1/2=1

Վարժ. 133

ա) cos23°-tg22°sin23°/sin8°+tg22°cos8°=√2

cos23°-sin22°/cos22°×sin23° / sin8°+sin22°/cos22°×cos8°=cos(23°+22°)/sin(22°+8°)=cos45°/sin30°=√2/2×2/1=√2

Վարժ. 137

ա) ( 5(m-2)/m³-8 – m+2/m²+2m+4 ) × 2m²+4m+8/m-3=( 5(m-2)/(m-2)×(m²+2m+4)-m+2/m²+2m+4)×2(m²+2m+4)/m-3=5-(m+2)/m²+2m+4×2(m²+2m+4)/m-3=-(m-3)×2/m-3=-1×2=-2

բ) (n+2/3n -2/n-2 -n-14/3n²-6n)÷n+2/6n×1/n-5=(n+2/3n-6n+n-14/3n×(n-2))×6n/n+2×1/n-5=(n+2/3-7/3n)×6n/n+2×1/n-5=n+2-7/3n×6n/n+2×1/n-5=n-5/3×6/n+2×1/n-5=2/n+2