To solve this equation, let's rewrite it step by step: 1. √2tanα = 1/2(1 - tan2α) 2. Simplify the right side: √2tanα = 1/2 - 1/2tan2α 3. Multiply both sides by 2 to eliminate the fraction: 2√2tanα = 1 - tan2α 4. Rearrange the terms: tan2α + 2√2tanα - 1 = 0 Now we have a quadratic equation in terms of tanα. To solve this equation, we can use the quadratic formula: tanα = (-b ± √(b2 - 4ac))/(2a) Where a = 1, b = 2√2, and c = -1. Plugging in these values and simplifying gives us: tanα = (-2√2 ± √(8 + 4))/2 tanα = (-2√2 ± √12)/2 tanα = -√2 ± √3 Therefore, there are two possible solutions for α: α = arctan(-√2 + √3) α = arctan(-√2 - √3)

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