有冇人可以教我做數(有關三角恆等式)

1:答案需用平方根號表示,不用計算機
a.(cos45 over sin45)+(sin30 over tan45)
= tan 45 + ( 1/2 over 1 )
=1 + 1/2
= 3/2

b.(1-sin45^2 over cos60)-tan 30^2
=( cos^(2) 45 over 1/2 ) - (1/平方根(3))^(2)
=( (平方根(2)/2)^(2) * 2) - 1/3
=( 2/4 * 2 ) - 1/3
=1 -1/3
=2/3

2.化簡:
sinθ^2 + sin(90-θ) 乘(sinθ over tan θ)
先睇右邊
sin(90-θ) 乘 sinθ over tanθ
= cosθ * sinθ over (sinθ/cosθ)
= cosθsinθ * cosθ/sinθ
= cos^(2)θ

成條式
sinθ^2 + sin(90-θ) 乘(sinθ over tan θ)
=sinθ^(2) + cos^(2)θ
=1

3.(使用代入法)
tan 25 = (h over 7500-x)----------(1)
tan 63 = (h over x)-------------(2)

其實我想問 7500 - x 有冇括號=.=\
我當佢有啦
from (1)
tan 25=(h over 7500-x)
h / tan 25 = 7500 - x
7500 - h / tan 25 = x ...(1)'

from (2)
tan 63 = (h over x)
h / tan 63 = x ...(2)'

Sub (2)' into (1)'
7500 - h / tan 25 = h / tan 63
7500 = h / tan 63 + h / tan 25
7500 = ( tan25 h + tan63 h ) / (tan25tan63)
之後按計數機
7500 = 2.428918164...h / 0.915180308...
6863.852315...= 2.428918164...h
h = 2825.888668...
h = 2826(Corr to nearest integer )

1a.
cos45 / sin45 + sin30 / tan45
root2 root2 1
= ----- 除 ----- + ---- 除 1
2 2 2

= 1 + 1/2
= 3/2


1b.
(1-sin45^2 over cos60)-tan 30^2
1- [(root2)/ 2 ]^2 1
= ------------------------ － [----------] ^2
1/2 root3

= 2 - 1 － 1/3
= 2/3


2.
sinθ^2 + sin(90-θ) 乘(sinθ over tan θ)
= sinθ^2 + cosθ乘 sinθ 除 tan θ
= sinθ^2 + cosθ乘 sinθ 乘 cosθ 除 sinθ
=sinθ^2 + cosθ^2
=1