Question

If Coso +Sino = p and sec o + Cosec =0=q , prove that q (p 2-1)=2p.

Answer 1

Step-by-step explanation:

$\huge\mathfrak\green{\bold{\underline{☘{ ℘ɧεŋσɱεŋศɭ}☘}}}$

$\red{\bold{\underline{\underline{QUESTION:-}}}}$

Q:-solve and verify the equation

$\frac{1}{3} x - 4 = x - ( \frac{1}{2} + \frac{x}{ 3} )$

$\huge\tt\underline\blue{Answer }$

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _✍️

══════════XXX═════════════

$⟹</p><p> \frac{1}{3} x - 4 = x - ( \frac{1}{2} + \frac{x}{3} )$

$⟹</p><p> \frac{x}{3} - 4 = x - ( \frac{3 + 2x}{6} )$

$⟹</p><p> \frac{x - 12}{3} = x - ( \frac{2x + 3}{6} )$

$⟹</p><p> \frac{x - 12}{3} = x - \frac{2x - 3}{6}$

$⟹</p><p> \frac{x - 12}{3} = \frac{6x - 2x - 3}{6}$

$⟹</p><p> \frac{x - 12}{3} = \frac{4x - 3}{6}$

cancelling 6( R.H.S) By 3 From L.H.S

$⟹ \frac{x - 12}{1} = \frac{4x - 3}{2} </p><p>$

$⟹</p><p>2(x - 12) = 4x - 3$

$⟹</p><p>2x - 24 = 4x - 3$

$⟹</p><p> - 24 + 3 = 4x - 2x$

$⟹</p><p> - 21 = 2x$

$⟹</p><p>x = - \frac{21}{2}$

CHECK:-

$⟹ \frac{ - \frac{21}{2} }{3} - 4 = - \frac{21}{2} - ( \frac{1}{2} + ( - ) \frac{ \frac{21}{2} }{3} )</p><p>$

$⟹</p><p> - \frac{21}{6} - 4 = - \frac{21}{2} - ( \frac{1}{2} - \frac{21}{6} )$

$⟹</p><p> - \frac{7}{2} - 4 = - \frac{21}{2} - ( \frac{1}{2} - \frac{7}{2} )$

$⟹</p><p> \frac{ - 7 - 8}{2} = - \frac{21}{2} - ( - \frac{6}{2} )$

$⟹ - \frac{15}{2} = - \frac{21}{2} - ( - 3) </p><p>$

$⟹</p><p> - \frac{15}{2} = - \frac{21}{2} + 3$

$⟹</p><p> - \frac{15}{2} = \frac{ - 21 + 6}{2} = - \frac{15}{2}$

THEREFORE,L.H.S=R.H.S

VERIFIED✔️

══════════XXX═════════════

HOPE IT HELPS YOU..

_____________________

Thankyou:)

Answer 2

Step-by-step explanation:

Step-by-step explanation:

\huge\mathfrak\green{\bold{\underline{☘{ ℘ɧεŋσɱεŋศɭ}☘}}}

☘℘ɧεŋσɱεŋศɭ☘

\red{\bold{\underline{\underline{QUESTION:-}}}}

QUESTION:−

Q:-solve and verify the equation

\frac{1}{3} x - 4 = x - ( \frac{1}{2} + \frac{x}{ 3} )

3

1

x−4=x−(

2

1

+

3

x

)

\huge\tt\underline\blue{Answer }

Answer

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _✍️

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⟹ < /p > < p > \frac{1}{3} x - 4 = x - ( \frac{1}{2} + \frac{x}{3} )⟹</p><p>

3

1

x−4=x−(

2

1

+

3

x

)

⟹ < /p > < p > \frac{x}{3} - 4 = x - ( \frac{3 + 2x}{6} )⟹</p><p>

3

x

−4=x−(

6

3+2x

)

⟹ < /p > < p > \frac{x - 12}{3} = x - ( \frac{2x + 3}{6} )⟹</p><p>

3

x−12

=x−(

6

2x+3

)

⟹ < /p > < p > \frac{x - 12}{3} = x - \frac{2x - 3}{6}⟹</p><p>

3

x−12

=x−

6

2x−3

⟹ < /p > < p > \frac{x - 12}{3} = \frac{6x - 2x - 3}{6}⟹</p><p>

3

x−12

=

6

6x−2x−3

⟹ < /p > < p > \frac{x - 12}{3} = \frac{4x - 3}{6}⟹</p><p>

3

x−12

=

6

4x−3

cancelling 6( R.H.S) By 3 From L.H.S

⟹ \frac{x - 12}{1} = \frac{4x - 3}{2} < /p > < p >⟹

1

x−12

=

2

4x−3

</p><p>

⟹ < /p > < p > 2(x - 12) = 4x - 3⟹</p><p>2(x−12)=4x−3

⟹ < /p > < p > 2x - 24 = 4x - 3⟹</p><p>2x−24=4x−3

⟹ < /p > < p > - 24 + 3 = 4x - 2x⟹</p><p>−24+3=4x−2x

⟹ < /p > < p > - 21 = 2x⟹</p><p>−21=2x

⟹ < /p > < p > x = - \frac{21}{2}⟹</p><p>x=−

2

21

CHECK:-

⟹ \frac{ - \frac{21}{2} }{3} - 4 = - \frac{21}{2} - ( \frac{1}{2} + ( - ) \frac{ \frac{21}{2} }{3} ) < /p > < p >⟹

3

−

2

21

−4=−

2

21

−(

2

1

+(−)

3

2

21

)</p><p>

⟹ < /p > < p > - \frac{21}{6} - 4 = - \frac{21}{2} - ( \frac{1}{2} - \frac{21}{6} )⟹</p><p>−

6

21

−4=−

2

21

−(

2

1

−

6

21

)

⟹ < /p > < p > - \frac{7}{2} - 4 = - \frac{21}{2} - ( \frac{1}{2} - \frac{7}{2} )⟹</p><p>−

2

7

−4=−

2

21

−(

2

1

−

2

7

)

⟹ < /p > < p > \frac{ - 7 - 8}{2} = - \frac{21}{2} - ( - \frac{6}{2} )⟹</p><p>

2

−7−8

=−

2

21

−(−

2

6

)

⟹ - \frac{15}{2} = - \frac{21}{2} - ( - 3) < /p > < p >⟹−

2

15

=−

2

21

−(−3)</p><p>

⟹ < /p > < p > - \frac{15}{2} = - \frac{21}{2} + 3⟹</p><p>−

2

15

=−

2

21

+3

⟹ < /p > < p > - \frac{15}{2} = \frac{ - 21 + 6}{2} = - \frac{15}{2}⟹</p><p>−

2

15

=

2

−21+6

=−

2

15

THEREFORE,L.H.S=R.H.S

VERIFIED✔️

══════════XXX═════════════

HOPE IT HELPS YOU..

_____________________

Thankyou:)