Question

1) 0.5 + sin^2 a + cos ^2 a2) 2-sin^2 a - cos ^2 a​

Answer 1

Основное тригонометрическое тождество:

$\fbox{sin^{2} \alpha + cos^{2} \: \alpha= 1 }$

тогда:

$1. \ 0.5 + sin^{2}a + cos^{2}a = 0.5 + 1 = 1.5 \\ 2. \: 2 - sin^{2}a - cos^{2}a = 2 - (sin^{2}a + cos^{2}a) = 2 - 1 = 1$

Answer 2

Let's simplify the given expressions step by step:

1. 0.5 + sin^2(a) + cos^2(a):

In trigonometry, the identity sin^2(a) + cos^2(a) = 1 holds true for any angle 'a'. So, the expression simplifies as follows:

0.5 + sin^2(a) + cos^2(a) = 0.5 + 1 = 1.5

2. 2 - sin^2(a) - cos^2(a):

Similarly, using the identity sin^2(a) + cos^2(a) = 1, the expression simplifies:

2 - sin^2(a) - cos^2(a) = 2 - 1 = 1

So, the simplified expressions are:

1. 0.5 + sin^2(a) + cos^2(a) = 1.5

2. 2 - sin^2(a) - cos^2(a) = 1