Решите пожалуйста
1.sin^2b-sin^2bcos^2b=
2.1+tga:1+ctga=tga
3. tga/tga+ctga=sina
4. tg(-a)ctga+sin^2(-a)=
1.sin^2b-sin^2bcos^2b=
2.1+tga:1+ctga=tga
3. tga/tga+ctga=sina
4. tg(-a)ctga+sin^2(-a)=
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Verified answer
1)sin²b-sin²bcos²b = sin²b(1-cos²b) = sin²bsin²b = sin⁴b
2)
(1+tga)/(1+ctga) = ((cosa+sina)/cosa)/((sina+cosa)/sina) =
= (cosa+sina)sina/cosa(sina+cosa) = sina/cosa = tga
3)
tga/(tga+ctga) = tga/(sina/cosa + cosa/sina) = tga/((sin²a+cos²a)/cosasina) =
= (sina/cosa)/(1/cosasina) = sinacosasina/cosa = sin²a
4)
tg(-a)ctga+sin²(-a) = -tgactga+(-sina)² = -1+sin²a = -cos²a