If cos α + cos β = 3 2   and   sin α + sin β = 1 2   and θ is the arithmetic mean of α   &   β , then sin 2 θ + cos 2 θ is equal to:

Question

If cos &#945; + cos &#946; = 3 2 &#160; and &#160; sin &#945; + sin &#946; = 1 2 &#160; and &#952; is the arithmetic mean of &#945; &#160; &#38; &#160; &#946; , then sin 2 &#952; + cos 2 &#952; is equal to:

Aicharya · Accepted Answer

Given cos &#160; &#945; &#160; + &#160; cos &#160; &#946; &#160; = &#160; 3 2 sin &#160; &#945; &#160; + &#160; sin &#160; &#946; &#160; = &#160; 1 2 &#8658; 2 c o s ( &#945; + &#946; 2 ) c o s ( &#945; - &#946; 2 ) = 3 2 ......(i) and 2 sin &#8289; ( &#945; + &#946; 2 ) c o s &#8289; ( &#945; - &#946; 2 )= 1 2 ....(ii) Dividing (ii) and (i) tan &#160; &#945; &#160; + &#160; &#946; 2 &#8756; &#160; &#160; tan &#8289; &#952; &#160; = 1 3 sin 2 &#952; + cos &#8289; 2 &#952; &#160; = 2 tan &#8289; &#952; 1 + tan 2 &#8289; &#952; + &#160; 1 - tan 2 &#8289; &#952; 1 + tan 2 &#8289; &#952; = 2 1 3 1 + 1 9 + 1 - 1 9 1 + 1 9 = &#160; 2 3 + 8 9 10 9 = 14 10 = 7 5

If cos α + cos β = 3 2   and   sin α + sin β = 1 2   and θ is the…

Solution

If cos &#945; + cos &#946; = 3 2 &#160; and &#160; sin &#945; + sin &#946; = 1 2 &#160; and &#952; is the…

Solution

If cos α + cos β = 3 2 and sin α + sin β = 1 2 and θ is the…