CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Proof by mathematical induction

If 0 < β < ...

Question

If $0 < β < α / 4, c o s (α + β) = 3 / 5 a n d cos (α - β) = 4 / 5$ find $s i n β α$ .

Open in App

Solution

$\begin{matrix} cos (α + β) = \frac{3}{5} \Rightarrow sin (α + β) = \frac{4}{5} . . . . . . . (i) c o s (α - β) = \frac{4}{5} sin (α - β) = cos (α + β) . . . . . (i i i) cos (α + β) = sin (90 - (α + β)) . . . . . . (i v) s u b (i v) i n (i i i) sin (α + β) = sin (90 - (α - β)) α + β = 90 - (α - β) β α = 90 sin (β α) = sin 90 \end{matrix}$

Suggest Corrections

thumbs-up

0

Similar questions

0 < β < α < \frac{π}{4}, cos (α + β) = \frac{3}{5}

cos (α - β) = \frac{4}{5}

sin 2 α

0 < α, β < \frac{π}{4}, cos (α + β) = \frac{4}{5}, sin (α - β) = \frac{5}{13}

tan 2 α =

cos (α + β) = 4 / 5, sin (α - β) = 5 / 13

α, β

0

\frac{π}{4}

tan 2 α

cos (α + β) = \frac{3}{5}, sin (α - β) = \frac{5}{13}

0 < α, β < \frac{π}{4},

tan (2 α)

cos (α + β) = \frac{4}{5}, sin (α - β) = \frac{5}{13}

α, β

lie between 0 and

\frac{π}{4}

tan 2 α =

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Mathematical Induction

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Proof by mathematical induction

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon