5sinx-12cosx-13sin3x-if - sin -112-13- then

The correct option is A sin(2x ϕ /2)=0 5 sin x 12 cos x= 13 sin 3x 5/13sin x 12/13cos x= sin 3x #160; #160; #160; #160; sin ϕ ...

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Byju's Answer

Standard XII

Mathematics

Composite Function

5sinx-12cosx=...

Question

5sinx-12cosx=-13sin3x,if $\emptyset$ = ${s i n}^{- 1}$ (12/13), then

sin(2x-

ϕ

/2)=0

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sin(x+

ϕ

/2)=0

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cos(x+

ϕ

/2)=0

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cos(2x+

ϕ

/2)=0

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Solution

The correct option is A sin(2x- $ϕ$ /2)=0
$5 s i n x - 12 c o s x = - 13 s i n 3 x$
$\frac{5}{13} s i n x - \frac{12}{13} c o s x = - s i n 3 x$ $s i n ϕ = \frac{12}{13}$
$\frac{12}{13} c o s x - \frac{5}{13} s i n x = s i n 3 x$
$s i n (ϕ - x) = s i n 3 x$
$s i n (ϕ - x) - s i n 3 x = 0$
$2 c o s (\frac{ϕ - x + 3 x}{2}) s i n (\frac{ϕ - x - 3 x}{2}) = 0$
$2 c o s x (\frac{ϕ}{2} + x) (s i n (\frac{ϕ}{2} - 2 x)) = 0$
$c o s (\frac{ϕ}{2} + x) = 0$ or $s i n (\frac{ϕ}{2} - 2 x) = 0$

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Similar questions

5 sin x - 12 cos x = - 13 sin 3 x

, if

ϕ = {sin}^{- 1} (\frac{12}{13})

, then

ϕ

is an acute angle such that

tan ϕ = \frac{2}{3}

then evaluate

(\frac{1 + tan ϕ}{sin ϕ + cos ϕ}) . (\frac{1 - cot ϕ}{sec ϕ + csc ϕ})

Q. Let

A = \{ϕ, \{ϕ\}, 1, \{1, ϕ\}, 2\}

. Which of the following are true?
(i)

ϕ \in A

(ii)

\{ϕ\} \in A

(iii)

\{1\} \in A

(iv)

\{2, ϕ\} \subset A

(v)

2 \subset A

(vi)

\{2 \{1\}\} ⊄ A

(vii)

\{\{2\}, \{1\}\} ⊄ A

(viii)

\{ϕ, \{ϕ\}, \{1, ϕ\}\} \subset A

(ix)

\{\{ϕ\}\} \subset A

Q. Prove that

{tan}^{4} ϕ + {tan}^{2} ϕ = {sec}^{4} ϕ - {sec}^{2} ϕ

, for

0^{\circ} \leq ϕ \leq 90^{\circ}

Q. Prove that the product of matrices

[\begin{matrix} {cos}^{2} θ & cos θ sin θ cos θ sin θ & {sin}^{2} θ \end{matrix}]

and

[\begin{matrix} {cos}^{2} ϕ & cos ϕ sin ϕ cos ϕ sin ϕ & {sin}^{2} ϕ \end{matrix}]

is the null matrix, when

θ

and

ϕ

differ by an odd multiple of

\frac{π}{2}

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5sinx-12cosx=-13sin3x,if ∅=sin−1(12/13), then

The correct option is A sin(2x-ϕ/2)=05sinx−12cosx=−13sin3x513sinx−1213cosx=−sin3x sinϕ=12131213cosx−513sinx=sin3xsin(ϕ−x)=sin3xsin(ϕ−x)−sin3x=02cos(ϕ−x+3x2)sin(ϕ−x−3x2)=02cosx(ϕ2+x)(sin(ϕ2−2x))=0cos(ϕ2+x)=0 or sin(ϕ2−2x)=0

5sinx-12cosx=-13sin3x,if $\emptyset$ = ${s i n}^{- 1}$ (12/13), then