Question

не могу решить 8 и 9

Answer 1

$8) \ frac{1-sin^4 alpha -cos^4 alpha }{cos^2 alpha } = frac{(1^2-(sin^2 alpha )^2)-cos^4 alpha }{cos^2 alpha } = \ \ = frac{(1-sin^2 alpha )(1+sin^2 alpha )-cos^4 alpha }{cos^2 alpha }= frac{cos^2 alpha (1+sin^2 alpha )-cos^4 alpha }{cos^2 alpha }= \ \ = frac{cos^2 alpha (1+sin^2 alpha )}{cos^2 alpha }- frac{cos^4 alpha }{cos^2 alpha }= \ \ =1+sin^2 alpha -cos^2 alpha =(1-cos^2 alpha )+sin^2 alpha =sin^2 alpha +sin^2 alpha =2sin^2 alpha$

$9. \ a) tg1*tg89=tg1*tg(90-1)=tg1*ctg1=tg1* frac{1}{ctg1}=1 \ \ b) tg3*tg87=tg3*tg(90-3)=tg3*ctg3=tg3* frac{1}{tg3}=1 \ \ tg1*tg3*tg5*...*tg89=1$