Question

Find the values of the constant a and b for which
sin x x cos x (5 tan x + 2 cot x) = a + b sin? x.

Answer 1

Answer:

$a = 2 \\ b = 3$

Step-by-step explanation:

$\sin(x) \cos(x) (5 \tan(x) + 2 \cot(x) ) = a + b$

$\sin(x). \cos(x) (5 \frac{ \sin(x) }{ \cos(x) } + 2 \frac{ \cos(x) }{ \sin(x) } )$

$5 { \sin(x) }^{2} + 2 { \cos(x) }^{2}$

$5 { \sin(x) }^{2} + 2(1 - { \sin(x) }^{2} ) \\ 5 { \sin(x) }^{2} + 2 - 2 { \sin(x) }^{2} \\ 3 { \sin(x) }^{2} + 2$

Now, comparing it with the form

$a + b ({ \sin(x) }^{2} )$

ᴡᴇ ɢᴇᴛ,

$a = 2 \\ b = 3$

ʜᴏᴩᴇ ɪᴛ ʜᴇʟᴩꜱ yᴏᴜ!!

ᴩʟᴇᴀꜱᴇ ᴍᴀʀᴋ ɪᴛ ᴀꜱ ʙʀᴀɪɴʟɪᴇꜱᴛ:)