![Simplify 60^ ecirc [(60^ ecirc + 2x) + (60^ ecirc - 2x)] given x = sqrt(t). Use the result from 7.2.1 and express in terms of t.](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1776360566482-2f2f746a0f86b64e.png&w=3840&q=75)
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's the solution for 7.2.2. 7.2.2 Step 1: Substitute the simplified expression from question 7.2.1 into the given expression. From 7.2.1, we found that (60^ + 2x) + (60^ - 2x) = sqrt(3) 2x. The expression to evaluate is 60^ [(60^ + 2x) + (60^ - 2x)]. Substitute the result from 7.2.1: 60^ [sqrt(3) 2x] Step 2: Evaluate 60^. We know that 60^ = sqrt(3). Substitute this value into the expression: sqrt(3) · sqrt(3) 2x = 3 2x Step 3: Use the double angle identity for 2x to express it in terms of x. The identity is 2x = 2 ^2 x - 1. Substitute this into the expression: 3 (2 ^2 x - 1) Step 4: Substitute the given value x = sqrt(t). 3 (2 (sqrt(t))^2 - 1) = 3 (2t - 1) Step 5: Simplify the expression. 3(2t - 1) = 6t - 3 The value of the expression in terms of t is: 6t - 3 What's next?