Q:

Find the two geometric means between 20 and 5. 7. Solve: 44-32-3 8. Develop the identity for sin 2.4 using the identity for sin(A+ B).

Accepted Solution

A:
Answer with explanation:1.Let a, and b be two numbers between 20 and 5 , which is in geometric progression.So,the series is as Follows =20 , a, b, 5Common ratio           [tex]=\frac{\text{Second term}}{\text{First term}}[/tex][tex]\frac{20}{a}=\frac{a}{b}=\frac{b}{5}\\\\b^2=5 a---(1)\\\\a^2=20 b\\\\\frac{b^4}{25}=20 b-----\text{Using 1}\\\\b^3=500\\\\b=(500)^{\frac{1}{3}}\\\\b=5\times (4)^{\frac{1}{3}}\\\\5a=25\times (4)^{\frac{2}{3}}\\\\a=5\times (4)^{\frac{2}{3}}[/tex]2. 44 -32-3=12-3=93.⇒Sin (2.4)=Sin(2+0.4)⇒Sin 2 ×Cos (0.4)+Cos 2 × Sin (0.4)⇒Sin (A+B)=Sin A×Cos B+Cos A×Sin B