The expression provided is:sin^2(2a) + cos^2(2a) + ctg^2(5a)
Given that:sin^2(θ) + cos^2(θ) = 1ctg(θ) = 1/tan(θ)
We can rewrite the expression using these identities:
sin^2(2a) + cos^2(2a) + ctg^2(5a)= 1 + 1 + (1/tan(5a))^2= 2 + cot^2(5a)
Therefore, the simplified expression is:2 + cot^2(5a)
The expression provided is:
sin^2(2a) + cos^2(2a) + ctg^2(5a)
Given that:
sin^2(θ) + cos^2(θ) = 1
ctg(θ) = 1/tan(θ)
We can rewrite the expression using these identities:
sin^2(2a) + cos^2(2a) + ctg^2(5a)
= 1 + 1 + (1/tan(5a))^2
= 2 + cot^2(5a)
Therefore, the simplified expression is:
2 + cot^2(5a)