Question

Please solve it fast. I will mark ka brainliest​

Answer 1

Answer:

i think it will really help u

Answer 2

${\boxed{\mathtt{\green{To\:Find}}}}$

$If \: \sin( \theta) + \csc( \theta) = 2$

$then \: { \sin( \theta) }^{15} - { \csc( \theta) }^{15} + 4 \sin( \theta) . \csc( \theta)$

${\boxed{\mathtt{\green{Solution}}}}$

We have given sin a + cosec a = 2

⇢ Cosec is reciprocal of Sine .So

$\implies \: \sin( \theta) + \frac{1}{ \sin( \theta) } = 2$

$\implies \: \frac{ { \sin( \theta) + 1}^{2} }{ \sin( \theta) } \: = \: 2$

$\implies \: { \sin( \theta) }^{2} + 1 \: = \: 2 \: \sin( \theta)$

$\implies \: { \sin( \theta) }^{2} - 2 \: \sin( \theta) \: + 1 \: = \: 0$

$\implies \: ( { \sin( \theta) - 1) }^{2} = 0$

$\boxed {\implies \: \sin( \theta) \: = \: 1}$

Now we have to put the value of sine in the question .

${(1)}^{15} \: - \frac{1}{( {1)}^{15} } \: + 4(1 \times \frac{1}{1} )$

$\implies \: 1 - 1 + 4$

${ \boxed{ \mathtt{ \implies \: 4 \: is \: the \: answer}}}$