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Answer:
Step-by-step explanation:
Required to prove that:
Sin θ(Sec θ + Cosec θ)= tan θ+1
Steps:
Recall sec θ= 1/cos θ and cosec θ=1/sin θ
Substitution into the Left Hand Side gives:
Sin θ(Sec θ + Cosec θ)
= Sin θ(1/cos θ + 1/sinθ )
Expanding the Brackets
=sinθ/cos θ + sinθ/sinθ
=tanθ+1 which is the Right Hand Side as required.
Note that from trigonometry sinθ/cosθ = tan θ
Answer:
20°
Step-by-step explanation:
40°, 70° and 90° are the measures of the three angles of the quadrilateral.
Measure of fourth angle of the Quadrilateral
= 360° - (40° + 70° + 90°)
= 360° - 200°
= 160°
Measure of angle 1 will be equal to the measure of the linear pair angle of 160° as they are corresponding angles.
Thus,
Alternate method:
![m\angle 1 = 180\degree- [360\degree-(40\degree+70\degree+90\degree)]](https://tex.z-dn.net/?f=m%5Cangle%201%20%3D%20180%5Cdegree-%20%5B360%5Cdegree-%2840%5Cdegree%2B70%5Cdegree%2B90%5Cdegree%29%5D)
![\implies m\angle 1 = 180\degree- [360\degree-200\degree]](https://tex.z-dn.net/?f=%5Cimplies%20m%5Cangle%201%20%3D%20180%5Cdegree-%20%5B360%5Cdegree-200%5Cdegree%5D)
Answer:
(-1, -7)
Step-by-step explanation:
Used desmos, also, in these situations I believe you can take the number inside the brackets and make it negative and keep the number outside the same to find the vertex.
