If a cos 3 α + 3a cos α sin 2 α = m and a sin 3 α + 3a cos 2 α sin α = n. if (m+n) 2/3 + (m − n) 2/3 = 2 λ a 2/3 , then find value of λ .
Text Solution
Verified by Experts1
(1) a cos 3 α + 3a cos α sin 2 α = m ... (i)
a sin 3 α + 3a cos 2 α sin α = n ... (ii)
then (m + n) 2/3 + (m – n) 2/3
= (a (cos 3 α + sin 3 α ) + 3a cos α sin α (cos α + sin α ) ) 2/3 +(a (cos 3 α – sin 3 α )+3a cos α sin α (sin α – cos α )) 2/3
= a 2/3 [{cos 3 α + sin 3 α + 3cos α sin α (cos α + sin α )} 2/3 + {cos 3 α – sin 3 α – 3cos α sin α (cos α – sin α )} 2/3 ]
= a 2/3 [{(cos α + sin α ) 3 } 2/3 + {(cos α – sin α ) 3 } 2/3 ]
= a 2/3 [(cos α + sin α ) 2 + (cos α – sin α ) 2 ] = a 2/3 [1 + 1] = 2a 2/3
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems