Question

cosec (90 + theta )+ x cos theta cot (90 + theta) = sin (90 + theta)

Answer 1

Answer:

Step-by-step explanation:

The given equation is:

$cosec(90+{\theta})+xcos{\theta}cot(90+{\theta})=sin(90+{\theta})$

Now, we know that $cosec(90+{\theta})=sec{\theta}$, $cot(90+{\theta})=-tan{\theta}$ and $sin(90+{\theta})=cos{\theta}$

Substituting these values in the given equation, we get

$sec{\theta}-xcos{\theta}tan{\theta}=cos{\theta}$

$\frac{1}{cos{\theta}}-xcos{\theta}\frac{sin{\theta}}{cos{\theta}}=cos{\theta}$

$\frac{1}{cos{\theta}}-xsin{\theta}=cos{\theta}$

$1-xsin{\theta}cos{\theta}=cos^2{\theta}$

$1-cos^2{\theta}=xsin{\theta}cos{\theta}$

$sin^2{\theta}=xsin{\theta}cos{\theta}$

$x=\frac{sin{\theta}}{cos{\theta}}$

$x=tan{\theta}$

Thus, the value of x is $tan{\theta}$.

Answer 2

Step-by-step explanation:

cosec(90+θ)+xcosθcot(90+θ)=sin(90+θ)

Now, we know that cosec(90+{\theta})=sec{\theta}cosec(90+θ)=secθ , cot(90+{\theta})=-tan{\theta}cot(90+θ)=−tanθ and sin(90+{\theta})=cos{\theta}sin(90+θ)=cosθ

Substituting these values in the given equation, we get

sec{\theta}-xcos{\theta}tan{\theta}=cos{\theta}secθ−xcosθtanθ=cosθ

\frac{1}{cos{\theta}}-xcos{\theta}\frac{sin{\theta}}{cos{\theta}}=cos{\theta}

cosθ

1

−xcosθ

cosθ

sinθ

=cosθ

\frac{1}{cos{\theta}}-xsin{\theta}=cos{\theta}

cosθ

1

−xsinθ=cosθ

1-xsin{\theta}cos{\theta}=cos^2{\theta}1−xsinθcosθ=cos

2

θ

1-cos^2{\theta}=xsin{\theta}cos{\theta}1−cos

2

θ=xsinθcosθ

sin^2{\theta}=xsin{\theta}cos{\theta}sin

2

θ=xsinθcosθ

x=\frac{sin{\theta}}{cos{\theta}}x=

cosθ

sinθ

x=tan{\theta}x=tanθ