Given that 6 cos θ + 8 sin θ ≡ R cos (θ + α) find the value of R - AQA - A-Level Maths Pure - Question 2 - 2020 - Paper 3

To express the equation in the form (R \cos(\theta + \alpha)), we can use the identity for combining sine and cosine. The general form is:

$R = \sqrt{A^2 + B^2}$

where (A) and (B) are the coefficients of (\cos(\theta)) and (\sin(\theta)), respectively. Here, (A = 6) and (B = 8).

Calculating (R):

$R = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10$

Thus, the value of (R) is 10.