Question

1+tg^2*a=1/cos^2*a
1+ctg^*2=1/sin^2*a
докажите пожалуйста!!!

Answer 1

а) 1+tg²@=1/cos²@
    1 + sin²@/cos²@ = 1/cos²@
    1 + (1-cos²@)/cos²@) = 1/cos²@
    (cos²@ + 1 - cos²@)/cos²@ = 1/cos²@
    1/cos²@ = 1/cos²@, ч.т.д.
б) 1+ctg²@=1/sin²@
    1 + cos²@/sin²@ = 1/sin²@
    1 + (1-sin²@)/sin²@) = 1/sin²@
    (sin²@ + 1 - sin²@)/sin²@ = 1/sin²@
    1/sin²@ = 1/sin²@, ч.т.д.