Please someone help me. It's about proving related to transformation of trigonometric ratios. Thank you!!

see explanation

Step-by-step explanation:

Using sum to product identities

cos x - cos y = - 2sin( )sin( ) = 2sin( )sin( )

cos x + cos y = 2cos( )cos( )

Note that

sin10° = sin(90 - 10)° = cos80°

Thus

← cancel 2 from numerator/ denominator

= ×

= tan45° × tan35° { tan45° = 1 ]

= 1 × tan35°

= tan35° ← as required

   see proof below

Step-by-step explanation:

* Use the following Co-function Identity: sin A = cos(90 - A)

* Use the following Sum to Product Identities:

 cos x - cos y = 2 sin [(x + y)/2] · sin [(x - y)/2]

 cos x + cos y = 2 cos [(x + y)/2] · cos [(x - y)/2]

* Use the Unit Circle to evaluate cos 45 = sin 45 = √2/2

Proof LHS → RHS

LHS = RHS:   tan 35 = tan 35  

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)

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step-by-step explanation: