Question

cos(n+1)α cos(n-1)α+sin(n+1)αsin(n-1)​

Answer 1

Here, as per the provided question we have to show that –

cos(n+1)α cos(n-1)α + sin(n+1)αsin(n-1)

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So, now let's learn here some of the most important basics symbol –

• α – This is the sign which shows the presence of 'alpha' in the given expression.

• sin – This is the symbol written for showing the presence of 'sin' from the provided expression.

• cos – This is the symbol written for showing the presence of 'cos' from the provided expression.

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Now, here let's start solving the given expression with the help of the provided information in the given question –

⟹ cos(n+1)α cos(n-1)α+sin(n+1)αsin(n-1)

Here, we will write the formula that is to be used here to perform the functions –

FORMULA USED :

• cos a cos b + sin a sin b = cos (a-b)

Therefore, as per the provided formula There's L.H.S that must be equals to R.H.S

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Now, we have here the values, we will show the value here :

• The value of a = (n+1)α
• The value of b = (n-1)α

[ substituting the values as per the provided appropriate formula ]

⟼ cos (a-b) = cos{ (n+1)α - (n-1)α }

⟼ cos (a-b) = cos {n(α) + α - n(α) + α }

⟼ cos (a-b) = cos{2α}

Hence, the value which is gained by the expression after solving the question = cos{2α}

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