Join now for JEE/NEET and also prepare for Boards Join now for JEE/NEET and also prepare for Boards. Register Now
Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
the maximum value of the expression 1/sin^2a+3sinacosa+5cos^2a the maximum value of the expression 1/sin^2a+3sinacosa+5cos^2a
the maximum value of the expression 1/sin^2a+3sinacosa+5cos^2a
multiply the numerator and the denominator by 2 numerator will become 2 & the denominator = 2sin^2a+6sinacosa+10cos^2a taking a (sin^2a + cos^2a) aside we get = sin^2a +6sinacosa +9cos^2a +sin^2a + cos^2a = (sina + 3 cosa)^2 + sin^2a +cos^2a = (sina + 3 cosa)^2 + 1 now the expression becomes 2/( (sina + 3 cosa)^2 + 1 ) for the maximum value of the expression the denominator must be minimum and for denominator to be minimum , (sina + 3 cosa)^2 must be minimum the minimum value of , (sina + 3 cosa)^2 can be zero when tana = -3 therefore the maximum value of the expression 2/( (sina + 3 cosa)^2 + 1 ) = 2/( 0 +1 ) = 2 if you want to aprreciate the solution , please click below on approve.
multiply the numerator and the denominator by 2
numerator will become 2 &
the denominator = 2sin^2a+6sinacosa+10cos^2a
taking a (sin^2a + cos^2a) aside we get
= sin^2a +6sinacosa +9cos^2a +sin^2a + cos^2a
= (sina + 3 cosa)^2 + sin^2a +cos^2a
= (sina + 3 cosa)^2 + 1
now the expression becomes 2/( (sina + 3 cosa)^2 + 1 )
for the maximum value of the expression the denominator must be minimum
and for denominator to be minimum , (sina + 3 cosa)^2 must be minimum
the minimum value of , (sina + 3 cosa)^2 can be zero when tana = -3
therefore the maximum value of the expression 2/( (sina + 3 cosa)^2 + 1 ) = 2/( 0 +1 )
= 2
if you want to aprreciate the solution , please click below on approve.
Dear Smit, Sanatan is right!! Its the right answer.
Dear Smit,
Sanatan is right!! Its the right answer.
cosec^2(a)+5(cos^2(a))
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -