If - - -900- let the maximum value of sin-sin- be m Find 8m

Let y=sinαsinβ =sinαsin ( 90^0 α nbsp; )=sinαcosα =1/2sin 2α which has the maximum value 1/2 when sin 2α =1 .Therefore, 8m=4 Ans: 4 ...

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Standard XII

Mathematics

Solving Simultaneous Trigonometric Equations

If α +β =90...

Question

If $α + β = 90^{0}$ , let the maximum value of $sin α sin β$ be $m$ Find $8 m$

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Solution

Let $y = sin α sin β = sin α sin (90^{0} - α) = sin α cos α = 1 / 2 sin 2 α$
which has the maximum value 1/2 when $sin 2 α = 1$ .
Therefore, $8 m = 4$
Ans: 4

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If α+β=900, let the maximum value of sinαsinβ be m Find 8m

Let y=sinαsinβ=sinαsin(900−α)=sinαcosα=1/2sin2αwhich has the maximum value 1/2 when sin2α=1.Therefore, 8m=4Ans: 4

If $α + β = 90^{0}$ , let the maximum value of $sin α sin β$ be $m$ Find $8 m$

Let $y = sin α sin β = sin α sin (90^{0} - α) = sin α cos α = 1 / 2 sin 2 α$
which has the maximum value 1/2 when $sin 2 α = 1$ .
Therefore, $8 m = 4$
Ans: 4